Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D383 | C2 | semidirect |
| 3. #27133840 | C2 | semidirect |
| 4. #27133827 | C2 | semidirect |
| 5. #27133826 | C2 | semidirect |
| 6. #27133823 | C2 | semidirect |
| 7. #27133821 | C2 | semidirect |
| 8. #27133820 | C2 | semidirect |
| 9. #27133817 | C2 | semidirect |
| 10. #27133799 | C2 | semidirect |
| 11. C22⋊Q8×C383 | C2 | semidirect |
| 83. C383 | #536 | semidirect |
| 94. C22⋊Q8 | D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259457 | 2 |
| C2×Q8×D383 | 2 |
| #27133840 | 2 |
| #27133827 | 2 |
| #27133826 | 2 |
| #27133823 | 2 |
| #27133821 | 2 |
| #27133820 | 2 |
| #27133817 | 2 |
| #27133799 | 2 |
| C22⋊Q8×C383 | 2 |
| #536 | 383 |