Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#20263355 | C2 | semidirect |
| 3. C4×Q8×D197 | C2 | semidirect |
| 4. #27161300 | C2 | semidirect |
| 5. #27161299 | C2 | semidirect |
| 6. #27161290 | C2 | semidirect |
| 7. #27161289 | C2 | semidirect |
| 8. #27161276 | C2 | semidirect |
| 9. #27161101 | C2 | semidirect |
| 10. #27161077 | C2 | semidirect |
| 11. #460×C197 | C2 | semidirect |
| 50. Q8×D197 | D4 | semidirect |
| 132. C4×C197 | #137 | semidirect |
| 146. C197 | #3037 | semidirect |
| 156. #460 | D197 | semidirect |
| 285. 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 |
| #27161627 | 2 |
| C4×Q8×D197 | 2 |
| #27161300 | 2 |
| #27161299 | 2 |
| #27161290 | 2 |
| #27161289 | 2 |
| #27161276 | 2 |
| #27161101 | 2 |
| #27161077 | 2 |
| #460×C197 | 2 |
| #3037 | 197 |