Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 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×#20259349 | C2 | semidirect |
| 2. #27133214 | C2 | semidirect |
| 3. C4×D4×D191 | C2 | semidirect |
| 4. #27132881 | C2 | semidirect |
| 5. #27132880 | C2 | semidirect |
| 6. #27132865 | C2 | semidirect |
| 7. #27132859 | C2 | semidirect |
| 8. #27132858 | C2 | semidirect |
| 9. #27132685 | C2 | semidirect |
| 10. #27132663 | C2 | semidirect |
| 11. #461×C191 | C2 | semidirect |
| 20. #20259319 | C22 | semidirect |
| 21. #20259311 | C22 | semidirect |
| 34. C4⋊(C191⋊C8) | C22 | semidirect |
| 35. Dic191⋊C8 | C22 | semidirect |
| 36. #20259246 | C22 | semidirect |
| 37. #20259244 | C22 | semidirect |
| 38. #20259242 | C22 | semidirect |
| 40. C4⋊Q8×C191 | C22 | semidirect |
| 42. C4⋊C8×C191 | C22 | semidirect |
| 43. #103×C191 | C22 | semidirect |
| 54. D4×D191 | D4 | semidirect |
| 146. C4×C191 | AGL(1,ℤ/8) | semidirect |
| 160. C191 | #3036 | semidirect |
| 168. #461 | D191 | semidirect |
| 182. C4⋊Q8 | C2×D191 | semidirect |
| 200. C4⋊C8 | C2×D191 | semidirect |
| 202. #103 | C2×D191 | semidirect |
| 311. C4 | #20259349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259349 | 2 |
| #27133214 | 2 |
| C4×D4×D191 | 2 |
| #27132881 | 2 |
| #27132880 | 2 |
| #27132865 | 2 |
| #27132859 | 2 |
| #27132858 | 2 |
| #27132685 | 2 |
| #27132663 | 2 |
| #461×C191 | 2 |
| #3036 | 191 |