Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
24030 conjugacy classes of subgroups; only the 4939 normal subgroups are shown.
This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 4939 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D13 |
| commutator, cosocle | C22×C13 | C26 |
| Frattini | C22 | C25×D13 |
| Fitting | C24×D4×C13 | C2 |
| socle | C25×C13 | C23 |
| hypercenter | C24×D4 | D13 |
| hypocenter | C13 | C23×#127 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C25 ◁ C24×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D52 | C2 | semidirect |
| 2. C24×C22⋊D13 | C2 | semidirect |
| 3. C22×#88194 | C2 | direct (N × H) |
| 4. C23×C4×Dic13 | C2 | semidirect |
| 5. C24×D4×C13 | C2 | semidirect |
| 9. C23×D4×C13 | C22 | semidirect |
| 12. C23×C22⋊D13 | C22 | semidirect |
| 15. C23×D52 | C22 | semidirect |
| 16. C2×#88194 | C22 | direct (N × H) |
| 17. C22×C4×Dic13 | C22 | semidirect |
| 26. C22×D4×C13 | C23 | semidirect |
| 27. C23×C4×C13 | D4 | semidirect |
| 30. C22×C22⋊D13 | C23 | semidirect |
| 31. C23×Dic13 | D4 | semidirect |
| 34. C22×D52 | C23 | semidirect |
| 35. #88194 | C23 | direct (N × H) |
| 36. C2×C4×Dic13 | C23 | semidirect |
| 50. C2×D4×C13 | C24 | semidirect |
| 51. C22×C4×C13 | C2×D4 | semidirect |
| 54. C2×C22⋊D13 | C24 | semidirect |
| 55. C22×Dic13 | C2×D4 | semidirect |
| 58. C2×D52 | C24 | semidirect |
| 59. C4×Dic13 | C24 | semidirect |
| 62. C24×D4 | D13 | semidirect |
| 68. C23×C13 | #127 | semidirect |
| 78. C2×C4×C13 | C22×D4 | semidirect |
| 81. C2×Dic13 | C22×D4 | semidirect |
| 91. C23×D4 | C2×D13 | semidirect |
| 99. C22×C13 | C2×#127 | semidirect |
| 106. C4×C13 | C23×D4 | semidirect |
| 107. Dic13 | C23×D4 | semidirect |
| 120. C22×D4 | C22×D13 | semidirect |
| 123. C23×C4 | C22⋊D13 | semidirect |
| 128. C2×C13 | C22×#127 | semidirect |
| 148. C2×D4 | C23×D13 | semidirect |
| 151. C22×C4 | C2×C22⋊D13 | semidirect |
| 154. C13 | C23×#127 | semidirect |
| 162. C23 | #88194 | direct (N × H) |
| 172. C2×C4 | C22×C22⋊D13 | semidirect |
| 180. C22 | C2×#88194 | direct (N × H) |
| 185. C4 | C23×C22⋊D13 | semidirect |
| 188. C2 | C22×#88194 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D52 | 2 |
| C24×C22⋊D13 | 2 |
| C22×#88194 | 2 |
| C23×C4×Dic13 | 2 |
| C24×D4×C13 | 2 |
| C23×#127 | 13 |