Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
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×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Frattini | C22 | C24×D19 |
| Fitting | C22×C42×C19 | C2 |
| hypercenter | C22×C42 | D19 |
| hypocenter | C19 | #3444 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927101 | C2 | semidirect |
| 2. #11927094 | C2 | semidirect |
| 3. #11927078 | C2 | semidirect |
| 4. #11927055 | C2 | semidirect |
| 5. C4×#64541 | C2 | semidirect |
| 6. C22×C42×C19 | C2 | semidirect |
| 18. #10597322 | C22 | semidirect |
| 19. #10597321 | C22 | semidirect |
| 20. #10597320 | C22 | semidirect |
| 21. C4×D76 | C22 | semidirect |
| 22. #10597318 | C22 | semidirect |
| 23. C42×D19 | C22 | semidirect |
| 24. #10597316 | C22 | semidirect |
| 25. #10597315 | C22 | semidirect |
| 26. C4×Dic38 | C22 | semidirect |
| 55. C2×C4×C19 | #41 | semidirect |
| 79. C22×C42 | D19 | semidirect |
| 103. C19 | #3444 | semidirect |
| 137. C2×C4 | #64541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927101 | 2 |
| #11927094 | 2 |
| #11927078 | 2 |
| #11927055 | 2 |
| C4×#64541 | 2 |
| C22×C42×C19 | 2 |
| #3444 | 19 |