Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic394 | C2 | semidirect |
| 2. C2×#20263356 | C2 | semidirect |
| 3. #27161234 | C2 | semidirect |
| 4. #27161217 | C2 | semidirect |
| 5. #27161087 | C2 | semidirect |
| 6. #27161043 | C2 | semidirect |
| 15. C2×#15691348 | C22 | semidirect |
| 16. C2×#15691346 | C22 | semidirect |
| 18. #20263249 | C22 | semidirect |
| 34. C2×Dic394 | D4 | semidirect |
| 95. C22×C197 | #137 | semidirect |
| 108. C197 | #3004 | semidirect |
| 204. C22 | #20263356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic394 | 2 |
| C2×#20263356 | 2 |
| #27161234 | 2 |
| #27161217 | 2 |
| #27161087 | 2 |
| #27161043 | 2 |
| #525×C197 | 2 |
| #3004 | 197 |