Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D197 | C2 | semidirect |
| 4. #27161290 | C2 | semidirect |
| 5. #27161288 | C2 | semidirect |
| 6. #27161286 | C2 | semidirect |
| 7. #27161284 | C2 | semidirect |
| 8. #27161282 | C2 | semidirect |
| 9. #27161101 | C2 | semidirect |
| 10. #27161086 | C2 | semidirect |
| 11. #461×C197 | C2 | semidirect |
| 131. C4×C197 | #137 | semidirect |
| 139. Dic197 | #137 | semidirect |
| 145. C197 | #3039 | semidirect |
| 155. #461 | D197 | semidirect |
| 283. C4 | #20263355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263355 | 2 |
| C4⋊Q8×D197 | 2 |
| C4×#15691357 | 2 |
| #27161290 | 2 |
| #27161288 | 2 |
| #27161286 | 2 |
| #27161284 | 2 |
| #27161282 | 2 |
| #27161101 | 2 |
| #27161086 | 2 |
| #461×C197 | 2 |
| #3039 | 197 |