Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #27133001 | C2 | semidirect |
| 3. #27132955 | C2 | semidirect |
| 4. #27132950 | C2 | semidirect |
| 5. #27132870 | C2 | semidirect |
| 6. #27132865 | C2 | semidirect |
| 8. #27132768 | C2 | semidirect |
| 9. #27132761 | C2 | semidirect |
| 10. #27132720 | C2 | semidirect |
| 11. #533×C191 | C2 | semidirect |
| 136. C191 | #3116 | semidirect |
| 138. #533 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15690287 | 2 |
| #27133001 | 2 |
| #27132955 | 2 |
| #27132950 | 2 |
| #27132870 | 2 |
| #27132865 | 2 |
| #27132823 | 2 |
| #27132768 | 2 |
| #27132761 | 2 |
| #27132720 | 2 |
| #533×C191 | 2 |
| #3116 | 191 |