Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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×#20263347 | C2 | semidirect |
| 2. #27161630 | C2 | semidirect |
| 3. C4×#15691357 | C2 | semidirect |
| 4. #27161304 | C2 | semidirect |
| 5. #27161296 | C2 | semidirect |
| 6. #27161286 | C2 | semidirect |
| 7. #27161280 | C2 | semidirect |
| 8. #27161274 | C2 | semidirect |
| 9. C4⋊C8×D197 | C2 | semidirect |
| 10. #27161074 | C2 | semidirect |
| 11. #461×C197 | C2 | semidirect |
| 47. #15691357 | D4 | semidirect |
| 136. C4×C197 | #135 | semidirect |
| 150. C197 | #3035 | semidirect |
| 158. #461 | D197 | semidirect |
| 292. C4 | #20263347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263347 | 2 |
| #27161630 | 2 |
| C4×#15691357 | 2 |
| #27161304 | 2 |
| #27161296 | 2 |
| #27161286 | 2 |
| #27161280 | 2 |
| #27161274 | 2 |
| C4⋊C8×D197 | 2 |
| #27161074 | 2 |
| #461×C197 | 2 |
| #3035 | 197 |