Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#20259352 | C2 | semidirect |
| 2. C2×#20259352 | C2 | semidirect |
| 3. #27133430 | C2 | semidirect |
| 4. #27132936 | C2 | semidirect |
| 5. #27132924 | C2 | semidirect |
| 6. #27132711 | C2 | semidirect |
| 7. #27132647 | C2 | semidirect |
| 8. C2×#20259240 | C2 | semidirect |
| 16. C2×#15690277 | C22 | semidirect |
| 18. C2×#15690275 | C22 | semidirect |
| 25. #20259257 | C22 | semidirect |
| 26. #20259241 | C22 | semidirect |
| 27. #20259240 | C22 | semidirect |
| 28. #20259239 | C22 | semidirect |
| 142. C191 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259352 | 2 |
| #27133430 | 2 |
| #27132936 | 2 |
| #27132924 | 2 |
| #27132711 | 2 |
| #27132647 | 2 |
| C2×#20259240 | 2 |
| #575×C191 | 2 |
| #3069 | 191 |