Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D191 | C2 | semidirect |
| 2. C2×#20259328 | C2 | semidirect |
| 3. #27133229 | C2 | semidirect |
| 4. #27132915 | C2 | semidirect |
| 5. #27132914 | C2 | semidirect |
| 6. #27132900 | C2 | semidirect |
| 7. #27132899 | C2 | semidirect |
| 8. #27132896 | C2 | semidirect |
| 9. #27132700 | C2 | semidirect |
| 10. #27132666 | C2 | semidirect |
| 11. #466×C191 | C2 | semidirect |
| 18. C2×#15690271 | C22 | semidirect |
| 20. C2×#15690270 | C22 | semidirect |
| 22. C2×C8×D191 | C22 | semidirect |
| 25. #20259297 | C22 | semidirect |
| 26. #20259296 | C22 | semidirect |
| 27. #20259293 | C22 | semidirect |
| 31. #20259256 | C22 | semidirect |
| 32. #20259253 | C22 | semidirect |
| 33. #20259244 | C22 | semidirect |
| 34. #20259243 | C22 | semidirect |
| 35. #20259242 | C22 | semidirect |
| 37. C22×C8×C191 | C22 | semidirect |
| 38. #121×C191 | C22 | semidirect |
| 39. #107×C191 | C22 | semidirect |
| 40. #102×C191 | C22 | semidirect |
| 65. C8×D191 | D4 | semidirect |
| 150. C191 | #3058 | semidirect |
| 160. #466 | D191 | semidirect |
| 175. C22×C8 | C2×D191 | semidirect |
| 181. #121 | C2×D191 | semidirect |
| 186. #107 | C2×D191 | semidirect |
| 191. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D191 | 2 |
| C2×#20259328 | 2 |
| #27133229 | 2 |
| #27132915 | 2 |
| #27132914 | 2 |
| #27132900 | 2 |
| #27132899 | 2 |
| #27132896 | 2 |
| #27132700 | 2 |
| #27132666 | 2 |
| #466×C191 | 2 |
| #3058 | 191 |