Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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 |
|---|---|---|
| 1. C2×#20263324 | C2 | semidirect |
| 4. #27160986 | C2 | semidirect |
| 5. #27160984 | C2 | semidirect |
| 6. #27160974 | C2 | semidirect |
| 7. #27160948 | C2 | semidirect |
| 36. C22×Dic197 | Q8 | semidirect |
| 99. C22×C197 | C4⋊Q8 | semidirect |
| 112. Dic197 | C22⋊Q8 | semidirect |
| 119. C197 | #2857 | semidirect |
| 219. C22 | #20263324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263324 | 2 |
| C2×#20263305 | 2 |
| C22×C4×Dic197 | 2 |
| #27160986 | 2 |
| #27160984 | 2 |
| #27160974 | 2 |
| #27160948 | 2 |
| #27160937 | 2 |
| C2×C22⋊Q8×C197 | 2 |
| #2857 | 197 |