Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D191 | C2 | semidirect |
| 4. #27132922 | C2 | semidirect |
| 5. #27132921 | C2 | semidirect |
| 6. #27132918 | C2 | semidirect |
| 7. #27132903 | C2 | semidirect |
| 8. #27132902 | C2 | semidirect |
| 9. #27132698 | C2 | semidirect |
| 10. #27132670 | C2 | semidirect |
| 11. #470×C191 | C2 | semidirect |
| 133. C191 | #3059 | semidirect |
| 141. #470 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D191 | 2 |
| C2×#20259330 | 2 |
| #27133236 | 2 |
| #27132922 | 2 |
| #27132921 | 2 |
| #27132918 | 2 |
| #27132903 | 2 |
| #27132902 | 2 |
| #27132698 | 2 |
| #27132670 | 2 |
| #470×C191 | 2 |
| #3059 | 191 |