Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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×#20263267 | C2 | semidirect |
| 2. #27161454 | C2 | semidirect |
| 3. D8×Dic197 | C2 | semidirect |
| 4. #27160897 | C2 | semidirect |
| 5. #27160881 | C2 | semidirect |
| 6. #27160880 | C2 | semidirect |
| 7. C2×D16×C197 | C2 | semidirect |
| 38. D8×C197 | D4 | semidirect |
| 74. Dic197 | D16 | semidirect |
| 81. C197 | #2206 | semidirect |
| 84. C2×D16 | D197 | semidirect |
| 115. D8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263267 | 2 |
| #27161454 | 2 |
| D8×Dic197 | 2 |
| #27160897 | 2 |
| #27160881 | 2 |
| #27160880 | 2 |
| C2×D16×C197 | 2 |
| #2206 | 197 |