Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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×#20263265 | C2 | semidirect |
| 2. #27161312 | C2 | semidirect |
| 3. #27160907 | C2 | semidirect |
| 4. #27160880 | C2 | semidirect |
| 5. C2×D16×C197 | C2 | semidirect |
| 27. C16×C197 | D4 | semidirect |
| 55. C197 | #2218 | semidirect |
| 57. C2×D16 | D197 | semidirect |
| 83. C16 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263265 | 2 |
| #27161312 | 2 |
| #27160907 | 2 |
| #27160880 | 2 |
| C2×D16×C197 | 2 |
| #2218 | 197 |