Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #27161101 | C2 | semidirect |
| 3. C4⋊C8×D197 | C2 | semidirect |
| 4. #27160826 | C2 | semidirect |
| 5. #27160824 | C2 | semidirect |
| 6. #27160823 | C2 | semidirect |
| 7. #331×C197 | C2 | semidirect |
| 98. C197 | #1547 | semidirect |
| 106. #331 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161627 | 2 |
| #27161101 | 2 |
| C4⋊C8×D197 | 2 |
| #27160826 | 2 |
| #27160824 | 2 |
| #27160823 | 2 |
| #331×C197 | 2 |
| #1547 | 197 |