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×#20263345 | C2 | semidirect |
| 2. #27161627 | C2 | semidirect |
| 3. C4×#15691357 | C2 | semidirect |
| 4. #27161300 | C2 | semidirect |
| 5. #27161292 | C2 | semidirect |
| 6. #27161290 | C2 | semidirect |
| 7. #27161284 | C2 | semidirect |
| 8. #27161276 | C2 | semidirect |
| 9. C4⋊C8×D197 | C2 | semidirect |
| 10. #27161072 | C2 | semidirect |
| 11. #459×C197 | C2 | semidirect |
| 47. #15691357 | D4 | semidirect |
| 135. C4×C197 | #135 | semidirect |
| 150. C197 | #3035 | semidirect |
| 160. #459 | D197 | semidirect |
| 292. C4 | #20263345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263345 | 2 |
| #27161627 | 2 |
| C4×#15691357 | 2 |
| #27161300 | 2 |
| #27161292 | 2 |
| #27161290 | 2 |
| #27161284 | 2 |
| #27161276 | 2 |
| C4⋊C8×D197 | 2 |
| #27161072 | 2 |
| #459×C197 | 2 |
| #3035 | 197 |