Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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. #27160904 | C2 | semidirect |
| 4. #27160884 | C2 | semidirect |
| 5. #27160882 | C2 | semidirect |
| 7. #367×C197 | C2 | semidirect |
| 65. C197 | #2237 | semidirect |
| 69. #367 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161321 | 2 |
| #27161116 | 2 |
| #27160904 | 2 |
| #27160884 | 2 |
| #27160882 | 2 |
| #27160858 | 2 |
| #367×C197 | 2 |
| #2237 | 197 |