Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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. #27161101 | C2 | semidirect |
| 3. #27160828 | C2 | semidirect |
| 4. #27160822 | C2 | semidirect |
| 5. #333×C197 | C2 | semidirect |
| 66. C197 | #1560 | semidirect |
| 71. #333 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161630 | 2 |
| #27161101 | 2 |
| #27160828 | 2 |
| #27160822 | 2 |
| #333×C197 | 2 |
| #1560 | 197 |