Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D191 | C2 | semidirect |
| 3. C2×#20259298 | C2 | semidirect |
| 4. #27132918 | C2 | semidirect |
| 5. #27132906 | C2 | semidirect |
| 6. #27132901 | C2 | semidirect |
| 7. #27132889 | C2 | semidirect |
| 8. #27132705 | C2 | semidirect |
| 9. #27132672 | C2 | semidirect |
| 10. #27132664 | C2 | semidirect |
| 11. C2×#137×C191 | C2 | semidirect |
| 33. #20259256 | C22 | semidirect |
| 34. #20259254 | C22 | semidirect |
| 35. #20259246 | C22 | semidirect |
| 36. #20259246 | C22 | semidirect |
| 37. #20259246 | C22 | semidirect |
| 38. #20259243 | C22 | semidirect |
| 42. C2×Q16×C191 | C22 | semidirect |
| 43. C2×SD16×C191 | C22 | semidirect |
| 90. M16×C191 | D4 | semidirect |
| 145. C2×D191 | #137 | semidirect |
| 163. C191 | #3056 | semidirect |
| 165. C2×#137 | D191 | semidirect |
| 180. C2×Q16 | C2×D191 | semidirect |
| 181. C2×SD16 | C2×D191 | semidirect |
| 236. M16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D191 | 2 |
| #27133170 | 2 |
| C2×#20259298 | 2 |
| #27132918 | 2 |
| #27132906 | 2 |
| #27132901 | 2 |
| #27132889 | 2 |
| #27132705 | 2 |
| #27132672 | 2 |
| #27132664 | 2 |
| C2×#137×C191 | 2 |
| #3056 | 191 |