Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #27160900 | C2 | semidirect |
| 4. #27160899 | C2 | semidirect |
| 5. #364×C197 | C2 | semidirect |
| 54. C197 | #2153 | semidirect |
| 60. #364 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D197 | 2 |
| #27161033 | 2 |
| #27160900 | 2 |
| #27160899 | 2 |
| #364×C197 | 2 |
| #2153 | 197 |