Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27133241 | C2 | semidirect |
| 2. #27132999 | C2 | semidirect |
| 3. #27132977 | C2 | semidirect |
| 4. #27132909 | C2 | semidirect |
| 5. #27132904 | C2 | semidirect |
| 6. #27132899 | C2 | semidirect |
| 7. #27132827 | C2 | semidirect |
| 8. #27132810 | C2 | semidirect |
| 9. #408×C191 | C2 | semidirect |
| 119. C191 | #3203 | semidirect |
| 129. #408 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133241 | 2 |
| #27132999 | 2 |
| #27132977 | 2 |
| #27132909 | 2 |
| #27132904 | 2 |
| #27132899 | 2 |
| #27132827 | 2 |
| #27132810 | 2 |
| #408×C191 | 2 |
| #3203 | 191 |