Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27161097 | C2 | semidirect |
| 3. #27161095 | C2 | semidirect |
| 4. #27161088 | C2 | semidirect |
| 5. #27161061 | C2 | semidirect |
| 6. #27161052 | C2 | semidirect |
| 7. #419×C197 | C2 | semidirect |
| 13. C2×#15691359 | C4 | semidirect |
| 18. C2×Q8×D197 | C4 | semidirect |
| 146. C197 | #1796 | semidirect |
| 152. #419 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263374 | 2 |
| #27161097 | 2 |
| #27161095 | 2 |
| #27161088 | 2 |
| #27161061 | 2 |
| #27161052 | 2 |
| #419×C197 | 2 |
| #1796 | 197 |