Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161383 | C2 | semidirect |
| 3. #27161383 | C2 | semidirect |
| 4. #27161371 | C2 | semidirect |
| 5. #27161361 | C2 | semidirect |
| 43. 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 |
|---|---|
| #27161556 | 2 |
| #27161383 | 2 |
| #27161371 | 2 |
| #27161361 | 2 |
| #27161119 | 2 |
| #27161115 | 2 |
| #27161106 | 2 |
| #27161087 | 2 |
| C2×#20263249 | 2 |
| #544×C197 | 2 |
| #3082 | 197 |