Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27133103 | C2 | semidirect |
| 2. C2×#20259266 | C2 | semidirect |
| 3. #27132938 | C2 | semidirect |
| 4. #27132476 | C2 | semidirect |
| 5. #27132470 | C2 | semidirect |
| 6. #27132447 | C2 | semidirect |
| 9. C2×Dic764 | C22 | semidirect |
| 13. #20259262 | C22 | semidirect |
| 14. C2×C191⋊C16 | C22 | semidirect |
| 15. #20259258 | C22 | semidirect |
| 91. C191 | #2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133103 | 2 |
| C2×#20259266 | 2 |
| #27132938 | 2 |
| #27132476 | 2 |
| #27132470 | 2 |
| #27132447 | 2 |
| #576×C191 | 2 |
| #2194 | 191 |