Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #27161430 | C2 | semidirect |
| 4. #27161415 | C2 | semidirect |
| 5. #27161375 | C2 | semidirect |
| 6. #27161320 | C2 | semidirect |
| 7. #27161290 | C2 | semidirect |
| 8. #27161237 | C2 | semidirect |
| 9. C4×Dic788 | C2 | semidirect |
| 10. C2×#20263251 | C2 | semidirect |
| 93. D4×C197 | Q16 | semidirect |
| 122. C197 | #3299 | semidirect |
| 208. D4 | Dic788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161786 | 2 |
| D4×Dic394 | 2 |
| #27161430 | 2 |
| #27161415 | 2 |
| #27161375 | 2 |
| #27161320 | 2 |
| #27161290 | 2 |
| #27161237 | 2 |
| C4×Dic788 | 2 |
| C2×#20263251 | 2 |
| C8×D4×C197 | 2 |
| #3299 | 197 |