Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161733 | C2 | semidirect |
| 2. #27161426 | C2 | semidirect |
| 3. #27161275 | C2 | semidirect |
| 4. #27161274 | C2 | semidirect |
| 5. #27160824 | C2 | semidirect |
| 6. #27160808 | C2 | semidirect |
| 7. D4⋊C8×C197 | C2 | semidirect |
| 71. D4×C197 | D8 | semidirect |
| 104. C197 | #1625 | semidirect |
| 112. D4⋊C8 | D197 | semidirect |
| 170. D4 | D1576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161733 | 2 |
| #27161426 | 2 |
| #27161275 | 2 |
| #27161274 | 2 |
| #27160824 | 2 |
| #27160808 | 2 |
| D4⋊C8×C197 | 2 |
| #1625 | 197 |