Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#20259281 | C2 | semidirect |
| 3. #27133005 | C2 | semidirect |
| 4. #27132999 | C2 | semidirect |
| 5. #27132994 | C2 | semidirect |
| 6. #27132988 | C2 | semidirect |
| 7. #27132982 | C2 | semidirect |
| 8. #27132977 | C2 | semidirect |
| 9. #27132701 | C2 | semidirect |
| 10. #27132660 | C2 | semidirect |
| 11. C2×C22⋊C8×C191 | C2 | semidirect |
| 30. #20259256 | C22 | semidirect |
| 31. #20259256 | C22 | semidirect |
| 32. #20259254 | C22 | semidirect |
| 33. #20259254 | C22 | semidirect |
| 34. #20259247 | C22 | semidirect |
| 35. #20259247 | C22 | semidirect |
| 36. #20259244 | C22 | semidirect |
| 37. #20259244 | C22 | semidirect |
| 143. C191 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133174 | 2 |
| C2×#20259281 | 2 |
| #27133005 | 2 |
| #27132999 | 2 |
| #27132994 | 2 |
| #27132988 | 2 |
| #27132982 | 2 |
| #27132977 | 2 |
| #27132701 | 2 |
| #27132660 | 2 |
| C2×C22⋊C8×C191 | 2 |
| #3091 | 191 |