Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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×#20259344 | C2 | semidirect |
| 2. #27133174 | C2 | semidirect |
| 3. #27132921 | C2 | semidirect |
| 4. #27132916 | C2 | semidirect |
| 5. #27132909 | C2 | semidirect |
| 6. #27132701 | C2 | semidirect |
| 7. #27132660 | C2 | semidirect |
| 8. C22×M16×C191 | C2 | semidirect |
| 11. C2×Dic764 | C22 | semidirect |
| 12. C2×#15690276 | C22 | semidirect |
| 13. C2×D1528 | C22 | semidirect |
| 20. #20259256 | C22 | semidirect |
| 21. #20259254 | C22 | semidirect |
| 22. #20259247 | C22 | semidirect |
| 23. #20259244 | C22 | semidirect |
| 56. C2×C8×C191 | D4 | semidirect |
| 105. C191 | #3054 | semidirect |
| 108. C22×M16 | D191 | semidirect |
| 156. 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×#20259344 | 2 |
| #27133174 | 2 |
| #27132921 | 2 |
| #27132916 | 2 |
| #27132909 | 2 |
| #27132701 | 2 |
| #27132660 | 2 |
| C22×M16×C191 | 2 |
| #3054 | 191 |