Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #27133211 | C2 | semidirect |
| 2. #27133210 | C2 | semidirect |
| 3. #27132954 | C2 | semidirect |
| 4. #27132953 | C2 | semidirect |
| 5. #27132951 | C2 | semidirect |
| 6. #27132915 | C2 | semidirect |
| 7. #27132913 | C2 | semidirect |
| 8. #27132856 | C2 | semidirect |
| 9. #27132855 | C2 | semidirect |
| 10. #27132685 | C2 | semidirect |
| 11. #459×C191 | C2 | semidirect |
| 150. C191 | #3253 | semidirect |
| 161. #459 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133211 | 2 |
| #27133210 | 2 |
| #27132954 | 2 |
| #27132953 | 2 |
| #27132951 | 2 |
| #27132915 | 2 |
| #27132913 | 2 |
| #27132856 | 2 |
| #27132855 | 2 |
| #27132685 | 2 |
| #459×C191 | 2 |
| #3253 | 191 |