Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27133459 | C2 | semidirect |
| 2. C2×#20259341 | C2 | semidirect |
| 3. #131×D191 | C2 | semidirect |
| 4. #27132939 | C2 | semidirect |
| 5. #27132938 | C2 | semidirect |
| 6. #27132930 | C2 | semidirect |
| 7. #27132925 | C2 | semidirect |
| 8. #27132924 | C2 | semidirect |
| 9. #108×D191 | C2 | semidirect |
| 10. #27132644 | C2 | semidirect |
| 11. #472×C191 | C2 | semidirect |
| 25. C2×Dic764 | C22 | semidirect |
| 26. C2×#15690275 | C22 | semidirect |
| 37. #20259258 | C22 | semidirect |
| 38. #20259257 | C22 | semidirect |
| 39. #20259240 | C22 | semidirect |
| 40. #20259240 | C22 | semidirect |
| 41. #20259239 | C22 | semidirect |
| 43. C2×D8×C191 | C22 | semidirect |
| 45. #108×C191 | C22 | semidirect |
| 46. #100×C191 | C22 | semidirect |
| 166. C191 | #3067 | semidirect |
| 174. #472 | D191 | semidirect |
| 195. C2×D8 | C2×D191 | semidirect |
| 209. #108 | C2×D191 | semidirect |
| 213. #100 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133459 | 2 |
| C2×#20259341 | 2 |
| #131×D191 | 2 |
| #27132939 | 2 |
| #27132938 | 2 |
| #27132930 | 2 |
| #27132925 | 2 |
| #27132924 | 2 |
| #108×D191 | 2 |
| #27132644 | 2 |
| #472×C191 | 2 |
| #3067 | 191 |