Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
42862 conjugacy classes of subgroups; only the 5451 normal subgroups are shown.
This group has 42862 conjugacy classes of subgroups — too many to draw. Only its 5451 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 | C27×C13 | C2 |
| socle | C25×C13 | C23 |
| hypercenter | C27 | D13 |
| hypocenter | C13 | C23×#120 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C25 ◁ C27 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C22⋊D13 | C2 | semidirect |
| 2. C22×#88207 | C2 | direct (N × H) |
| 3. C23×C22⋊Dic13 | C2 | semidirect |
| 4. C27×C13 | C2 | semidirect |
| 7. C26×C13 | C22 | semidirect |
| 8. C25×D13 | C22 | semidirect |
| 10. C23×C22⋊D13 | C22 | semidirect |
| 11. C24×Dic13 | C22 | semidirect |
| 12. C2×#88207 | C22 | direct (N × H) |
| 13. C22×C22⋊Dic13 | C22 | semidirect |
| 17. C25×C13 | D4 | semidirect |
| 20. C25×C13 | C23 | semidirect |
| 22. C24×D13 | C23 | semidirect |
| 24. C22×C22⋊D13 | C23 | semidirect |
| 26. C23×Dic13 | C23 | semidirect |
| 27. #88207 | C23 | direct (N × H) |
| 28. C2×C22⋊Dic13 | C23 | semidirect |
| 35. C24×C13 | C2×D4 | semidirect |
| 38. C24×C13 | C24 | semidirect |
| 41. C23×D13 | C24 | semidirect |
| 43. C2×C22⋊D13 | C24 | semidirect |
| 45. C22×Dic13 | C24 | semidirect |
| 46. C22⋊Dic13 | C24 | semidirect |
| 47. C27 | D13 | semidirect |
| 55. C23×C13 | #120 | semidirect |
| 57. C23×C13 | C22×D4 | semidirect |
| 62. C22×D13 | C25 | semidirect |
| 65. C2×Dic13 | C25 | semidirect |
| 69. C26 | C2×D13 | semidirect |
| 78. C22×C13 | C2×#120 | semidirect |
| 80. C22×C13 | C23×D4 | semidirect |
| 90. C25 | C22⋊D13 | semidirect |
| 93. C25 | C22×D13 | semidirect |
| 101. C2×C13 | C22×#120 | semidirect |
| 112. C24 | C2×C22⋊D13 | semidirect |
| 115. C24 | C23×D13 | semidirect |
| 121. C13 | C23×#120 | semidirect |
| 129. C23 | #88207 | direct (N × H) |
| 131. C23 | C22×C22⋊D13 | semidirect |
| 142. C22 | C2×#88207 | direct (N × H) |
| 144. C22 | C23×C22⋊D13 | semidirect |
| 149. C2 | C22×#88207 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C22⋊D13 | 2 |
| C22×#88207 | 2 |
| C23×C22⋊Dic13 | 2 |
| C27×C13 | 2 |
| C23×#120 | 13 |