Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
564 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 189 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. #27160985 | C2 | semidirect |
| 3. #27160977 | C2 | semidirect |
| 4. #27160963 | C2 | semidirect |
| 45. C22×C4×C197 | Q8 | semidirect |
| 102. C197 | #2855 | semidirect |
| 142. C22×C4 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263305 | 2 |
| #27160985 | 2 |
| #27160977 | 2 |
| #27160963 | 2 |
| #27160952 | 2 |
| #27160942 | 2 |
| #27160939 | 2 |
| C22×C42×C197 | 2 |
| #2855 | 197 |