Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #27161561 | C2 | semidirect |
| 3. #27161192 | C2 | semidirect |
| 4. #27161190 | C2 | semidirect |
| 5. #27161186 | C2 | semidirect |
| 6. C4×#15691345 | C2 | semidirect |
| 7. #27161164 | C2 | semidirect |
| 8. #106×D197 | C2 | semidirect |
| 9. #27161079 | C2 | semidirect |
| 10. #27161036 | C2 | semidirect |
| 11. #441×C197 | C2 | semidirect |
| 13. #20263349 | C4 | semidirect |
| 41. #15691359 | C2×C4 | semidirect |
| 49. #15691345 | C2×C4 | semidirect |
| 50. D1576 | C2×C4 | semidirect |
| 54. C8×D197 | C2×C4 | semidirect |
| 65. Q16×C197 | C2×C4 | semidirect |
| 114. C197 | #2952 | semidirect |
| 121. #441 | D197 | semidirect |
| 165. Q16 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| #27161561 | 2 |
| #27161192 | 2 |
| #27161190 | 2 |
| #27161186 | 2 |
| C4×#15691345 | 2 |
| #27161164 | 2 |
| #106×D197 | 2 |
| #27161079 | 2 |
| #27161036 | 2 |
| #441×C197 | 2 |
| #2952 | 197 |