Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27161483 | C2 | semidirect |
| 3. #27161457 | C2 | semidirect |
| 4. #27161428 | C2 | semidirect |
| 7. Q16×Dic197 | C2 | semidirect |
| 8. #27161173 | C2 | semidirect |
| 9. #27161171 | C2 | semidirect |
| 77. C2×Dic197 | Q16 | semidirect |
| 114. C197 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161631 | 2 |
| #27161483 | 2 |
| #27161457 | 2 |
| #27161428 | 2 |
| #27161320 | 2 |
| #27161318 | 2 |
| Q16×Dic197 | 2 |
| #27161173 | 2 |
| #27161171 | 2 |
| C2×C8×Dic197 | 2 |
| #467×C197 | 2 |
| #3170 | 197 |