Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#20259355 | C2 | semidirect |
| 2. C2×#20259330 | C2 | semidirect |
| 4. #27133239 | C2 | semidirect |
| 5. #27132922 | C2 | semidirect |
| 6. #27132910 | C2 | semidirect |
| 7. #27132905 | C2 | semidirect |
| 8. #27132893 | C2 | semidirect |
| 9. #27132657 | C2 | semidirect |
| 10. C2×#20259245 | C2 | semidirect |
| 11. #428×C191 | C2 | semidirect |
| 77. M16×C191 | D4 | semidirect |
| 143. C191 | #3063 | semidirect |
| 153. #428 | D191 | semidirect |
| 210. M16 | D764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259355 | 2 |
| C2×#20259330 | 2 |
| #27133244 | 2 |
| #27133239 | 2 |
| #27132922 | 2 |
| #27132910 | 2 |
| #27132905 | 2 |
| #27132893 | 2 |
| #27132657 | 2 |
| C2×#20259245 | 2 |
| #428×C191 | 2 |
| #3063 | 191 |