Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D31 |
| commutator, socle, cosocle | C22×C31 | C25 |
| Frattini | C22 | C24×D31 |
| Fitting | C22×C42×C31 | C2 |
| hypercenter | C22×C42 | D31 |
| hypocenter | C31 | #3444 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14521606 | C2 | semidirect |
| 2. #14521599 | C2 | semidirect |
| 3. #14521583 | C2 | semidirect |
| 4. #14521560 | C2 | semidirect |
| 5. C4×#92495 | C2 | semidirect |
| 6. C22×C42×C31 | C2 | semidirect |
| 18. #11758453 | C22 | semidirect |
| 19. #11758452 | C22 | semidirect |
| 20. #11758451 | C22 | semidirect |
| 21. C4×D124 | C22 | semidirect |
| 22. #11758449 | C22 | semidirect |
| 23. C42×D31 | C22 | semidirect |
| 24. #11758447 | C22 | semidirect |
| 25. #11758446 | C22 | semidirect |
| 26. C4×Dic62 | C22 | semidirect |
| 55. C2×C4×C31 | #41 | semidirect |
| 79. C22×C42 | D31 | semidirect |
| 103. C31 | #3444 | semidirect |
| 137. C2×C4 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521606 | 2 |
| #14521599 | 2 |
| #14521583 | 2 |
| #14521560 | 2 |
| C4×#92495 | 2 |
| C22×C42×C31 | 2 |
| #3444 | 31 |