Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161630 | C2 | semidirect |
| 2. #27161456 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161316 | C2 | semidirect |
| 5. #27161161 | C2 | semidirect |
| 6. C4×C8×D197 | C2 | semidirect |
| 7. #500×C197 | C2 | semidirect |
| 58. C4×D197 | D8 | semidirect |
| 65. C8×C197 | #41 | semidirect |
| 85. C197 | #3169 | semidirect |
| 88. #500 | D197 | semidirect |
| 151. C8 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161630 | 2 |
| #27161456 | 2 |
| #27161427 | 2 |
| #27161316 | 2 |
| #27161161 | 2 |
| C4×C8×D197 | 2 |
| #500×C197 | 2 |
| #3169 | 197 |