Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
13646 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 13646 conjugacy classes of subgroups — too many to draw. Only its 1539 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 | C23×C13 | C25 |
| Frattini | C23 | C24×D13 |
| Fitting | C22×C13×#95 | C2 |
| socle | C25×C13 | C23 |
| hypercenter | C22×#95 | D13 |
| hypocenter | C13 | C22×#392 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C25 ◁ C22×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D52 | C2 | semidirect |
| 2. C23×#6103 | C2 | semidirect |
| 3. C2×#11718332 | C2 | direct (N × H) |
| 4. C22×C13×#95 | C2 | semidirect |
| 10. C23×D52 | C22 | semidirect |
| 12. C22×#6103 | C22 | semidirect |
| 13. C2×C13×#95 | C22 | semidirect |
| 14. #11718332 | C22 | direct (N × H) |
| 20. C24×D13 | D4 | semidirect |
| 23. C23×C4×C13 | D4 | semidirect |
| 30. C22×D52 | C23 | semidirect |
| 32. C2×#6103 | C23 | semidirect |
| 33. C13×#95 | C23 | semidirect |
| 48. C23×D13 | C2×D4 | semidirect |
| 52. C22×C4×C13 | C2×D4 | semidirect |
| 64. C22×#95 | D13 | semidirect |
| 82. C22×D13 | C22×D4 | semidirect |
| 85. C2×C4×C13 | C22×D4 | semidirect |
| 98. C2×#95 | C2×D13 | semidirect |
| 99. C22×C13 | #392 | semidirect |
| 128. C23×C4 | D52 | semidirect |
| 132. #95 | C22×D13 | semidirect |
| 133. C2×C13 | C2×#392 | semidirect |
| 161. C22×C4 | C2×D52 | semidirect |
| 164. C13 | C22×#392 | semidirect |
| 188. C2×C4 | C22×D52 | semidirect |
| 195. C22 | #11718332 | direct (N × H) |
| 205. C2 | C2×#11718332 | 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 |
| C23×#6103 | 2 |
| C2×#11718332 | 2 |
| C22×C13×#95 | 2 |
| C22×#392 | 13 |