Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 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×D19 |
| commutator, socle, cosocle | C22×C19 | C25 |
| Fitting | C19×#519 | C2 |
| hypercenter | #519 | D19 |
| hypocenter | C19 | #3487 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597433 | C2 | semidirect |
| 2. C22×#64545 | C2 | semidirect |
| 3. #11927216 | C2 | semidirect |
| 4. #11927206 | C2 | semidirect |
| 5. #11927113 | C2 | semidirect |
| 6. #11927056 | C2 | semidirect |
| 7. C19×#519 | C2 | semidirect |
| 12. C2×#64545 | C22 | semidirect |
| 13. C2×Q8×D19 | C22 | semidirect |
| 17. C4×Q8×C19 | C22 | semidirect |
| 19. #10597343 | C22 | semidirect |
| 20. #10597341 | C22 | semidirect |
| 21. #10597341 | C22 | semidirect |
| 24. #10597321 | C22 | semidirect |
| 25. #10597320 | C22 | semidirect |
| 26. C4×D76 | C22 | semidirect |
| 28. C2×Q8×C19 | D4 | semidirect |
| 89. #519 | D19 | semidirect |
| 111. C4×Q8 | C2×D19 | semidirect |
| 114. C19 | #3487 | semidirect |
| 121. C2×Q8 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597433 | 2 |
| C22×#64545 | 2 |
| #11927216 | 2 |
| #11927206 | 2 |
| #11927113 | 2 |
| #11927056 | 2 |
| C19×#519 | 2 |
| #3487 | 19 |