Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #27132957 | C2 | semidirect |
| 4. #27132955 | C2 | semidirect |
| 7. #27132874 | C2 | semidirect |
| 8. #27132873 | C2 | semidirect |
| 9. #27132872 | C2 | semidirect |
| 11. #477×C191 | C2 | semidirect |
| 96. C4×D191 | Q16 | semidirect |
| 129. C191 | #3249 | semidirect |
| 135. #477 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #27133217 | 2 |
| #27132957 | 2 |
| #27132955 | 2 |
| #27132905 | 2 |
| #27132903 | 2 |
| #27132874 | 2 |
| #27132873 | 2 |
| #27132872 | 2 |
| C4⋊C8×D191 | 2 |
| #477×C191 | 2 |
| #3249 | 191 |