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. C22×#15690274 | C2 | semidirect |
| 2. C2×#20259329 | C2 | semidirect |
| 4. #27132911 | C2 | semidirect |
| 5. #27132894 | C2 | semidirect |
| 6. #27132699 | C2 | semidirect |
| 7. #27132672 | C2 | semidirect |
| 8. #27132667 | C2 | semidirect |
| 9. #536×C191 | C2 | semidirect |
| 16. C2×#15690271 | C22 | semidirect |
| 18. C22×C191⋊C8 | C22 | semidirect |
| 24. #20259255 | C22 | semidirect |
| 25. #20259253 | C22 | semidirect |
| 26. #20259246 | C22 | semidirect |
| 33. C22⋊Q8×C191 | C22 | semidirect |
| 46. C2×C191⋊C8 | D4 | semidirect |
| 120. C191 | #3057 | semidirect |
| 124. #536 | D191 | semidirect |
| 147. C22⋊Q8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690274 | 2 |
| C2×#20259329 | 2 |
| #27133227 | 2 |
| #27132911 | 2 |
| #27132894 | 2 |
| #27132699 | 2 |
| #27132672 | 2 |
| #27132667 | 2 |
| #536×C191 | 2 |
| #3057 | 191 |