Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161364 | C2 | semidirect |
| 3. #27161361 | C2 | semidirect |
| 5. #27161289 | C2 | semidirect |
| 6. #27161286 | C2 | semidirect |
| 104. C197 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| #27161364 | 2 |
| #27161361 | 2 |
| #27161335 | 2 |
| #27161289 | 2 |
| #27161286 | 2 |
| #27161103 | 2 |
| #533×C197 | 2 |
| #3255 | 197 |