Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D31 |
| commutator, socle, cosocle | C22×C31 | C25 |
| Fitting | C23×Q8×C31 | C2 |
| hypercenter | C23×Q8 | D31 |
| hypocenter | C31 | #3486 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11758564 | C2 | semidirect |
| 2. Q8×C22⋊D31 | C2 | semidirect |
| 3. #14521710 | C2 | semidirect |
| 4. #14521623 | C2 | semidirect |
| 5. #14521560 | C2 | semidirect |
| 6. #14521527 | C2 | semidirect |
| 7. C23×Q8×C31 | C2 | semidirect |
| 14. C2×#92499 | C22 | semidirect |
| 15. C2×Q8×D31 | C22 | semidirect |
| 18. #11758524 | C22 | semidirect |
| 19. #11758523 | C22 | semidirect |
| 20. Q8×Dic31 | C22 | semidirect |
| 21. #11758521 | C22 | semidirect |
| 30. C2×Q8×C31 | D4 | semidirect |
| 76. C22×C31 | 2−1+4 | semidirect |
| 85. C23×Q8 | D31 | semidirect |
| 115. C31 | #3486 | semidirect |
| 123. C2×Q8 | C22⋊D31 | semidirect |
| 165. C22 | #11758564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758564 | 2 |
| Q8×C22⋊D31 | 2 |
| #14521710 | 2 |
| #14521623 | 2 |
| #14521560 | 2 |
| #14521527 | 2 |
| C23×Q8×C31 | 2 |
| #3486 | 31 |