Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#20259343 | C2 | semidirect |
| 2. #27133214 | C2 | semidirect |
| 3. C4×#15690286 | C2 | semidirect |
| 4. #27132888 | C2 | semidirect |
| 5. #27132880 | C2 | semidirect |
| 6. #27132870 | C2 | semidirect |
| 7. #27132864 | C2 | semidirect |
| 8. #27132858 | C2 | semidirect |
| 9. C4⋊C8×D191 | C2 | semidirect |
| 10. #27132658 | C2 | semidirect |
| 11. #461×C191 | C2 | semidirect |
| 47. #15690286 | D4 | semidirect |
| 136. C4×C191 | #135 | semidirect |
| 150. C191 | #3035 | semidirect |
| 158. #461 | D191 | semidirect |
| 292. C4 | #20259343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259343 | 2 |
| #27133214 | 2 |
| C4×#15690286 | 2 |
| #27132888 | 2 |
| #27132880 | 2 |
| #27132870 | 2 |
| #27132864 | 2 |
| #27132858 | 2 |
| C4⋊C8×D191 | 2 |
| #27132658 | 2 |
| #461×C191 | 2 |
| #3035 | 191 |