Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161389 | C2 | semidirect |
| 4. #27161385 | C2 | semidirect |
| 5. #27161373 | C2 | semidirect |
| 6. #27161363 | C2 | semidirect |
| 44. C2×Dic394 | Q8 | semidirect |
| 116. C197 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161556 | 2 |
| #27161389 | 2 |
| #27161385 | 2 |
| #27161373 | 2 |
| #27161363 | 2 |
| #27161122 | 2 |
| #27161105 | 2 |
| #27161087 | 2 |
| C2×#20263251 | 2 |
| #427×C197 | 2 |
| #3082 | 197 |