Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. #27133234 | C2 | semidirect |
| 4. #27132921 | C2 | semidirect |
| 5. #27132909 | C2 | semidirect |
| 6. #27132904 | C2 | semidirect |
| 7. #27132892 | C2 | semidirect |
| 8. #27132705 | C2 | semidirect |
| 9. #27132660 | C2 | semidirect |
| 10. C2×#20259247 | C2 | semidirect |
| 11. C2×#131×C191 | C2 | semidirect |
| 79. M16×C191 | D4 | semidirect |
| 143. C191 | #3063 | semidirect |
| 146. C2×#131 | D191 | semidirect |
| 210. M16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259355 | 2 |
| #27133241 | 2 |
| #27133234 | 2 |
| #27132921 | 2 |
| #27132909 | 2 |
| #27132904 | 2 |
| #27132892 | 2 |
| #27132705 | 2 |
| #27132660 | 2 |
| C2×#20259247 | 2 |
| C2×#131×C191 | 2 |
| #3063 | 191 |