Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
310 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D383 |
| commutator, socle, cosocle | C22×C383 | C24 |
| Frattini | C22 | C23×D383 |
| Fitting | C2×C42×C383 | C2 |
| hypercenter | C2×C42 | D383 |
| hypocenter | C383 | #532 |
| LCS | G ▷ C22×C383 ▷ C383 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20259457 | C2 | semidirect |
| 2. #27133841 | C2 | semidirect |
| 3. #27133838 | C2 | semidirect |
| 4. #27133829 | C2 | semidirect |
| 5. #27133815 | C2 | semidirect |
| 6. C4×D1532 | C2 | semidirect |
| 7. C2×C42×C383 | C2 | semidirect |
| 30. C2×C4×C383 | D4 | semidirect |
| 43. C4×C383 | #41 | semidirect |
| 49. C383 | #532 | semidirect |
| 57. C2×C42 | D383 | semidirect |
| 80. C2×C4 | D1532 | semidirect |
| 94. C4 | #20259457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259457 | 2 |
| #27133841 | 2 |
| #27133838 | 2 |
| #27133829 | 2 |
| #27133815 | 2 |
| C4×D1532 | 2 |
| C2×C42×C383 | 2 |
| #532 | 383 |