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×#20263358 | C2 | semidirect |
| 3. C4×Q8×D197 | C2 | semidirect |
| 4. #27161304 | C2 | semidirect |
| 5. #27161303 | C2 | semidirect |
| 6. #27161286 | C2 | semidirect |
| 7. #27161280 | C2 | semidirect |
| 8. #27161279 | C2 | semidirect |
| 9. #27161101 | C2 | semidirect |
| 10. #27161079 | C2 | semidirect |
| 11. #462×C197 | C2 | semidirect |
| 49. Q8×D197 | D4 | semidirect |
| 133. C4×C197 | #137 | semidirect |
| 146. C197 | #3037 | semidirect |
| 154. #462 | D197 | semidirect |
| 285. C4 | #20263358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263358 | 2 |
| #27161630 | 2 |
| C4×Q8×D197 | 2 |
| #27161304 | 2 |
| #27161303 | 2 |
| #27161286 | 2 |
| #27161280 | 2 |
| #27161279 | 2 |
| #27161101 | 2 |
| #27161079 | 2 |
| #462×C197 | 2 |
| #3037 | 197 |