Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 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. C22×#15691348 | C2 | semidirect |
| 3. #27161556 | C2 | semidirect |
| 4. #27161298 | C2 | semidirect |
| 5. #27161286 | C2 | semidirect |
| 6. #27161106 | C2 | semidirect |
| 7. #27161088 | C2 | semidirect |
| 111. C197 | #3044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| C22×#15691348 | 2 |
| #27161556 | 2 |
| #27161298 | 2 |
| #27161286 | 2 |
| #27161106 | 2 |
| #27161088 | 2 |
| #27161075 | 2 |
| #536×C197 | 2 |
| #3044 | 197 |