Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27132681 | C2 | semidirect |
| 3. #27132668 | C2 | semidirect |
| 4. #27132636 | C2 | semidirect |
| 5. #27132433 | C2 | semidirect |
| 6. #27132419 | C2 | semidirect |
| 7. #518×C191 | C2 | semidirect |
| 11. C2×#15690275 | C4 | semidirect |
| 12. C2×#15690272 | C4 | semidirect |
| 29. C2×Dic382 | C2×C4 | semidirect |
| 30. C2×D764 | C2×C4 | semidirect |
| 40. C2×C191⋊C8 | C2×C4 | semidirect |
| 115. C191 | #1904 | semidirect |
| 118. #518 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259348 | 2 |
| #27132681 | 2 |
| #27132668 | 2 |
| #27132636 | 2 |
| #27132433 | 2 |
| #27132419 | 2 |
| #518×C191 | 2 |
| #1904 | 191 |