Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
222 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 35 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. #27160803 | C2 | semidirect |
| 3. #342×C197 | C2 | semidirect |
| 4. C22×D788 | C4 | semidirect |
| 8. #20263233 | C4 | semidirect |
| 88. C197 | #1343 | semidirect |
| 91. #342 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27160988 | 2 |
| #27160803 | 2 |
| #342×C197 | 2 |
| #1343 | 197 |