Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D19 |
| commutator, cosocle | C16×C19 | C23 |
| Frattini | C16 | C22×D19 |
| Fitting | C19×SD64 | C2 |
| socle | C2×C19 | C2×D16 |
| hypercenter | SD64 | D19 |
| hypocenter | C19 | #2263 |
| LCS | G ▷ C16×C19 ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11926977 | C2 | semidirect |
| 2. D16×D19 | C2 | semidirect |
| 3. #11926381 | C2 | semidirect |
| 4. D608 | C2 | semidirect |
| 5. #11926379 | C2 | semidirect |
| 6. #11926377 | C2 | semidirect |
| 7. C19×SD64 | C2 | semidirect |
| 10. C19×Q32 | C22 | semidirect |
| 15. D304 | C22 | semidirect |
| 17. C19×C32 | C22 | semidirect |
| 18. C19⋊C32 | C22 | semidirect |
| 53. SD64 | D19 | semidirect |
| 64. Q32 | C2×D19 | semidirect |
| 72. C32 | C2×D19 | semidirect |
| 73. C19 | #2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11926977 | 2 |
| D16×D19 | 2 |
| #11926381 | 2 |
| D608 | 2 |
| #11926379 | 2 |
| #11926377 | 2 |
| C19×SD64 | 2 |
| #2263 | 19 |