Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20259328 | C2 | semidirect |
| 2. #27133237 | C2 | semidirect |
| 4. #27132906 | C2 | semidirect |
| 5. #27132889 | C2 | semidirect |
| 6. #27132701 | C2 | semidirect |
| 7. #27132672 | C2 | semidirect |
| 8. #27132668 | C2 | semidirect |
| 9. C22×SD16×C191 | C2 | semidirect |
| 13. C2×#15690270 | C22 | semidirect |
| 14. C2×C8×D191 | C22 | semidirect |
| 20. #20259298 | C22 | semidirect |
| 25. #20259256 | C22 | semidirect |
| 26. #20259254 | C22 | semidirect |
| 27. #20259246 | C22 | semidirect |
| 68. C2×C8×C191 | D4 | semidirect |
| 120. C191 | #3057 | semidirect |
| 122. C22×SD16 | D191 | semidirect |
| 180. C2×C8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259328 | 2 |
| #27133237 | 2 |
| #27133230 | 2 |
| #27132906 | 2 |
| #27132889 | 2 |
| #27132701 | 2 |
| #27132672 | 2 |
| #27132668 | 2 |
| C22×SD16×C191 | 2 |
| #3057 | 191 |