Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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. #27133874 | C2 | semidirect |
| 3. #27133871 | C2 | semidirect |
| 4. #27133829 | C2 | semidirect |
| 5. #27133769 | C2 | semidirect |
| 6. #27133757 | C2 | semidirect |
| 7. #104×C383 | C2 | semidirect |
| 11. C2×Dic766 | C22 | semidirect |
| 20. #20259441 | C22 | semidirect |
| 23. M16×C383 | C22 | semidirect |
| 24. C42×C383 | C22 | semidirect |
| 64. C383 | #455 | semidirect |
| 71. #104 | D383 | semidirect |
| 87. M16 | C2×D383 | semidirect |
| 89. C42 | C2×D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133887 | 2 |
| #27133874 | 2 |
| #27133871 | 2 |
| #27133829 | 2 |
| #27133769 | 2 |
| #27133757 | 2 |
| #104×C383 | 2 |
| #455 | 383 |