Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C23×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C31×#126 | C2 |
| hypercenter | #126 | D31 |
| hypocenter | C31 | #560 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#126 | C2 | semidirect |
| 2. #11758472 | C2 | semidirect |
| 3. #11758471 | C2 | semidirect |
| 4. #11758461 | C2 | semidirect |
| 5. #11758459 | C2 | semidirect |
| 6. #11758453 | C2 | semidirect |
| 7. #11758451 | C2 | semidirect |
| 12. C2×D124 | C22 | semidirect |
| 13. C2×C4×D31 | C22 | semidirect |
| 14. C4⋊C4×C31 | C22 | semidirect |
| 16. C42×C31 | C22 | semidirect |
| 19. (C2×D31)⋊C4 | C22 | semidirect |
| 20. Dic31⋊C4 | C22 | semidirect |
| 53. #126 | D31 | semidirect |
| 58. C31 | #560 | semidirect |
| 66. C4⋊C4 | C2×D31 | semidirect |
| 71. C42 | C2×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#126 | 2 |
| #11758472 | 2 |
| #11758471 | 2 |
| #11758461 | 2 |
| #11758459 | 2 |
| #11758453 | 2 |
| #11758451 | 2 |
| #560 | 31 |