Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. C22⋊C8×D197 | C2 | semidirect |
| 3. #27160941 | C2 | semidirect |
| 4. #27160816 | C2 | semidirect |
| 5. #27160814 | C2 | semidirect |
| 6. #27160812 | C2 | semidirect |
| 7. #328×C197 | C2 | semidirect |
| 8. C2×#15691359 | C4 | semidirect |
| 12. #20263302 | C4 | semidirect |
| 13. #20263301 | C4 | semidirect |
| 18. #20263284 | C4 | semidirect |
| 127. C197 | #1516 | semidirect |
| 133. #328 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161592 | 2 |
| C22⋊C8×D197 | 2 |
| #27160941 | 2 |
| #27160816 | 2 |
| #27160814 | 2 |
| #27160812 | 2 |
| #328×C197 | 2 |
| #1516 | 197 |