Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
184 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 55 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. #27161280 | C2 | semidirect |
| 3. #27161209 | C2 | semidirect |
| 4. #27160822 | C2 | semidirect |
| 5. #334×C197 | C2 | semidirect |
| 47. C8×C197 | SD16 | semidirect |
| 62. C197 | #1688 | semidirect |
| 67. #334 | D197 | semidirect |
| 110. C8 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161456 | 2 |
| #27161280 | 2 |
| #27161209 | 2 |
| #27160822 | 2 |
| #334×C197 | 2 |
| #1688 | 197 |