Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#20259344 | C2 | semidirect |
| 2. C22×#15690270 | C2 | semidirect |
| 3. #27133175 | C2 | semidirect |
| 4. #27132922 | C2 | semidirect |
| 5. #27132917 | C2 | semidirect |
| 6. #27132910 | C2 | semidirect |
| 7. #27132657 | C2 | semidirect |
| 8. #427×C191 | C2 | semidirect |
| 12. C2×Dic764 | C22 | semidirect |
| 13. C2×#15690276 | C22 | semidirect |
| 14. C2×D1528 | C22 | semidirect |
| 24. #20259245 | C22 | semidirect |
| 25. #20259242 | C22 | semidirect |
| 28. #107×C191 | C22 | semidirect |
| 29. #106×C191 | C22 | semidirect |
| 54. C2×C8×C191 | D4 | semidirect |
| 105. C191 | #3054 | semidirect |
| 113. #427 | D191 | semidirect |
| 132. #107 | C2×D191 | semidirect |
| 133. #106 | C2×D191 | semidirect |
| 157. C2×C8 | D764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259344 | 2 |
| C22×#15690270 | 2 |
| #27133175 | 2 |
| #27132922 | 2 |
| #27132917 | 2 |
| #27132910 | 2 |
| #27132657 | 2 |
| #427×C191 | 2 |
| #3054 | 191 |