Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27161156 | C2 | semidirect |
| 3. #27160806 | C2 | semidirect |
| 4. #27160800 | C2 | semidirect |
| 5. #334×C197 | C2 | semidirect |
| 41. C8×C197 | M16 | semidirect |
| 55. C197 | #1594 | semidirect |
| 59. #334 | D197 | semidirect |
| 97. C8 | #15691341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1576 | 2 |
| #27161156 | 2 |
| #27160806 | 2 |
| #27160800 | 2 |
| #334×C197 | 2 |
| #1594 | 197 |