Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 1. #27133218 | C2 | semidirect |
| 3. #27133016 | C2 | semidirect |
| 4. #27133015 | C2 | semidirect |
| 5. #27133014 | C2 | semidirect |
| 6. #27133009 | C2 | semidirect |
| 7. #27132656 | C2 | semidirect |
| 8. C4×C8×D191 | C2 | semidirect |
| 9. #486×C191 | C2 | semidirect |
| 111. C191 | #3131 | semidirect |
| 119. #486 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133218 | 2 |
| #27133211 | 2 |
| #27133016 | 2 |
| #27133015 | 2 |
| #27133014 | 2 |
| #27133009 | 2 |
| #27132656 | 2 |
| C4×C8×D191 | 2 |
| #486×C191 | 2 |
| #3131 | 191 |