Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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. #27161035 | C2 | semidirect |
| 4. #27160849 | C2 | semidirect |
| 8. C2×#15691342 | C4 | semidirect |
| 11. C22×#13096802 | C4 | semidirect |
| 13. #20263245 | C4 | semidirect |
| 14. #20263243 | C4 | semidirect |
| 74. C197 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161063 | 2 |
| #27161035 | 2 |
| #27160849 | 2 |
| #410×C197 | 2 |
| #1757 | 197 |