Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161684 | C2 | semidirect |
| 2. #27161379 | C2 | semidirect |
| 3. #27161376 | C2 | semidirect |
| 4. #27161330 | C2 | semidirect |
| 5. #27161313 | C2 | semidirect |
| 6. #27161274 | C2 | semidirect |
| 7. #27161271 | C2 | semidirect |
| 8. #27161106 | C2 | semidirect |
| 9. #540×C197 | C2 | semidirect |
| 106. C197 | #3259 | semidirect |
| 109. #540 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161684 | 2 |
| #27161379 | 2 |
| #27161376 | 2 |
| #27161330 | 2 |
| #27161313 | 2 |
| #27161274 | 2 |
| #27161271 | 2 |
| #27161106 | 2 |
| #540×C197 | 2 |
| #3259 | 197 |