Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20259353 | C2 | semidirect |
| 2. C22×#15690274 | C2 | semidirect |
| 4. #27132885 | C2 | semidirect |
| 5. #27132863 | C2 | semidirect |
| 6. #27132690 | C2 | semidirect |
| 7. #27132667 | C2 | semidirect |
| 8. #27132657 | C2 | semidirect |
| 9. #519×C191 | C2 | semidirect |
| 13. C2×#15690277 | C22 | semidirect |
| 16. C2×#15690274 | C22 | semidirect |
| 23. C4⋊(C191⋊C8) | C22 | semidirect |
| 24. #20259245 | C22 | semidirect |
| 26. #20259242 | C22 | semidirect |
| 29. C4×Q8×C191 | C22 | semidirect |
| 55. C2×Q8×C191 | D4 | semidirect |
| 116. C191 | #3043 | semidirect |
| 121. #519 | D191 | semidirect |
| 142. C4×Q8 | C2×D191 | semidirect |
| 156. C2×Q8 | D764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259353 | 2 |
| C22×#15690274 | 2 |
| #27133232 | 2 |
| #27132885 | 2 |
| #27132863 | 2 |
| #27132690 | 2 |
| #27132667 | 2 |
| #27132657 | 2 |
| #519×C191 | 2 |
| #3043 | 191 |