Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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×#20259301 | C2 | semidirect |
| 3. #27132999 | C2 | semidirect |
| 4. #27132977 | C2 | semidirect |
| 5. #27132909 | C2 | semidirect |
| 6. #27132816 | C2 | semidirect |
| 7. #27132804 | C2 | semidirect |
| 8. #407×C191 | C2 | semidirect |
| 9. C22×Dic382 | C22 | semidirect |
| 12. C2×#15690276 | C22 | semidirect |
| 16. #20259301 | C22 | semidirect |
| 22. C2×C4⋊Dic191 | C22 | semidirect |
| 26. #20259256 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 28. #20259244 | C22 | semidirect |
| 30. C2×M16×C191 | C22 | semidirect |
| 32. C22⋊C8×C191 | C22 | semidirect |
| 129. C191 | #3193 | semidirect |
| 138. #407 | D191 | semidirect |
| 144. C2×M16 | C2×D191 | semidirect |
| 162. C22⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259301 | 2 |
| C2×#20259296 | 2 |
| #27132999 | 2 |
| #27132977 | 2 |
| #27132909 | 2 |
| #27132816 | 2 |
| #27132804 | 2 |
| #407×C191 | 2 |
| #3193 | 191 |