Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #27133197 | C2 | semidirect |
| 2. #27133065 | C2 | semidirect |
| 3. #27133047 | C2 | semidirect |
| 4. #27133018 | C2 | semidirect |
| 5. #27132921 | C2 | semidirect |
| 7. #27132909 | C2 | semidirect |
| 8. #27132776 | C2 | semidirect |
| 9. #27132771 | C2 | semidirect |
| 10. #27132765 | C2 | semidirect |
| 11. C4×M16×C191 | C2 | semidirect |
| 109. C191 | #3183 | semidirect |
| 121. C4×M16 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133197 | 2 |
| #27133065 | 2 |
| #27133047 | 2 |
| #27133018 | 2 |
| #27132921 | 2 |
| #27132916 | 2 |
| #27132909 | 2 |
| #27132776 | 2 |
| #27132771 | 2 |
| #27132765 | 2 |
| C4×M16×C191 | 2 |
| #3183 | 191 |