Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27161627 | C2 | semidirect |
| 4. #27161460 | C2 | semidirect |
| 5. #27161458 | C2 | semidirect |
| 6. #27161455 | C2 | semidirect |
| 7. #27161452 | C2 | semidirect |
| 8. C4×C8×D197 | C2 | semidirect |
| 9. #492×C197 | C2 | semidirect |
| 47. C8×D197 | D4 | semidirect |
| 91. C4×C197 | #135 | semidirect |
| 101. C197 | #3147 | semidirect |
| 110. #492 | D197 | semidirect |
| 196. 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 |
| #27161627 | 2 |
| #27161460 | 2 |
| #27161458 | 2 |
| #27161455 | 2 |
| #27161452 | 2 |
| C4×C8×D197 | 2 |
| #492×C197 | 2 |
| #3147 | 197 |