Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×#20259320 | C2 | semidirect |
| 3. #27133034 | C2 | semidirect |
| 4. #27133012 | C2 | semidirect |
| 5. #27132867 | C2 | semidirect |
| 6. #27132866 | C2 | semidirect |
| 7. #27132804 | C2 | semidirect |
| 8. #27132802 | C2 | semidirect |
| 9. #27132801 | C2 | semidirect |
| 10. #27132713 | C2 | semidirect |
| 11. #448×C191 | C2 | semidirect |
| 99. C2×Dic191 | SD16 | semidirect |
| 146. C191 | #3206 | semidirect |
| 157. #448 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133208 | 2 |
| C2×#20259320 | 2 |
| #27133034 | 2 |
| #27133012 | 2 |
| #27132867 | 2 |
| #27132866 | 2 |
| #27132804 | 2 |
| #27132802 | 2 |
| #27132801 | 2 |
| #27132713 | 2 |
| #448×C191 | 2 |
| #3206 | 191 |