Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 1. C2×#20259456 | C2 | semidirect |
| 2. C2×#20259446 | C2 | semidirect |
| 3. C2×#20259442 | C2 | semidirect |
| 4. #27133816 | C2 | semidirect |
| 5. #27133764 | C2 | semidirect |
| 6. (C2×D383)⋊C8 | C2 | semidirect |
| 7. #102×C383 | C2 | semidirect |
| 26. Dic766 | D4 | semidirect |
| 39. D4×C383 | D4 | semidirect |
| 64. C383 | #449 | semidirect |
| 71. #102 | D383 | semidirect |
| 98. D4 | D1532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259456 | 2 |
| C2×#20259446 | 2 |
| C2×#20259442 | 2 |
| #27133816 | 2 |
| #27133764 | 2 |
| (C2×D383)⋊C8 | 2 |
| #102×C383 | 2 |
| #449 | 383 |