Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27161129 | C2 | semidirect |
| 3. #27160943 | C2 | semidirect |
| 4. #27160814 | C2 | semidirect |
| 5. #27160813 | C2 | semidirect |
| 6. #27160812 | C2 | semidirect |
| 7. #327×C197 | C2 | semidirect |
| 9. #20263325 | C4 | semidirect |
| 10. #20263322 | C4 | semidirect |
| 14. D4×Dic197 | C4 | semidirect |
| 15. #20263288 | C4 | semidirect |
| 119. C197 | #1517 | semidirect |
| 127. #327 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161624 | 2 |
| #27161129 | 2 |
| #27160943 | 2 |
| #27160814 | 2 |
| #27160813 | 2 |
| #27160812 | 2 |
| #327×C197 | 2 |
| #1517 | 197 |