Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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. C22×#15690276 | C2 | semidirect |
| 2. #27133234 | C2 | semidirect |
| 4. #27132909 | C2 | semidirect |
| 5. #27132892 | C2 | semidirect |
| 6. #27132701 | C2 | semidirect |
| 7. #27132673 | C2 | semidirect |
| 8. #27132669 | C2 | semidirect |
| 9. C2×#131×C191 | C2 | semidirect |
| 20. #20259301 | C22 | semidirect |
| 25. #20259256 | C22 | semidirect |
| 26. #20259254 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 32. C2×M16×C191 | C22 | semidirect |
| 34. C22×C8×C191 | C22 | semidirect |
| 67. C2×C8×C191 | D4 | semidirect |
| 120. C191 | #3057 | semidirect |
| 123. C2×#131 | D191 | semidirect |
| 139. C2×M16 | C2×D191 | semidirect |
| 141. C22×C8 | C2×D191 | semidirect |
| 179. C2×C8 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690276 | 2 |
| #27133234 | 2 |
| #27133227 | 2 |
| #27132909 | 2 |
| #27132892 | 2 |
| #27132701 | 2 |
| #27132673 | 2 |
| #27132669 | 2 |
| C2×#131×C191 | 2 |
| #3057 | 191 |