Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×D383 |
| commutator, socle, cosocle | C22×C383 | C24 |
| Fitting | C22⋊Q8×C383 | C2 |
| hypercenter | C22⋊Q8 | D383 |
| hypocenter | C383 | #538 |
| LCS | G ▷ C22×C383 ▷ C383 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27133836 | C2 | semidirect |
| 2. #27133830 | C2 | semidirect |
| 3. #27133826 | C2 | semidirect |
| 4. #27133816 | C2 | semidirect |
| 5. #27133815 | C2 | semidirect |
| 6. #27133811 | C2 | semidirect |
| 7. (C22⋊D383)⋊C4 | C2 | semidirect |
| 8. C2×(C2×D383)⋊C4 | C2 | semidirect |
| 9. C22⋊Q8×C383 | C2 | semidirect |
| 13. C2×D1532 | C22 | semidirect |
| 16. C2×C4×D383 | C22 | semidirect |
| 17. C4⋊Dic383 | C22 | semidirect |
| 18. Dic383⋊C4 | C22 | semidirect |
| 23. (C2×D383)⋊C4 | C22 | semidirect |
| 24. (C2×D383)⋊C4 | C22 | semidirect |
| 25. C4×Dic383 | C22 | semidirect |
| 26. C2×Q8×C383 | C22 | semidirect |
| 28. C4⋊C4×C383 | C22 | semidirect |
| 29. C4⋊C4×C383 | C22 | semidirect |
| 74. C383 | #538 | semidirect |
| 79. C22⋊Q8 | D383 | semidirect |
| 86. C2×Q8 | C2×D383 | semidirect |
| 96. C4⋊C4 | C2×D383 | semidirect |
| 97. C4⋊C4 | C2×D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133836 | 2 |
| #27133830 | 2 |
| #27133826 | 2 |
| #27133816 | 2 |
| #27133815 | 2 |
| #27133811 | 2 |
| (C22⋊D383)⋊C4 | 2 |
| C2×(C2×D383)⋊C4 | 2 |
| C22⋊Q8×C383 | 2 |
| #538 | 383 |