Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#20263250 | C2 | semidirect |
| 5. C2×C8×Dic197 | C2 | semidirect |
| 6. #27160944 | C2 | semidirect |
| 7. C2×#103×C197 | C2 | semidirect |
| 11. #20263315 | C4 | semidirect |
| 111. C197 | #1958 | semidirect |
| 115. C2×#103 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263315 | 2 |
| C2×#20263250 | 2 |
| C2×#20263248 | 2 |
| C2×#20263246 | 2 |
| C2×C8×Dic197 | 2 |
| #27160944 | 2 |
| C2×#103×C197 | 2 |
| #1958 | 197 |