Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4⋊C4×D197 | C2 | semidirect |
| 3. C2×#20263247 | C2 | semidirect |
| 4. C2×#20263238 | C2 | semidirect |
| 5. #27160842 | C2 | semidirect |
| 6. #27160841 | C2 | semidirect |
| 7. C2×#102×C197 | C2 | semidirect |
| 13. #20263297 | C4 | semidirect |
| 47. C4⋊Dic197 | C2×C4 | semidirect |
| 48. C4⋊Dic197 | D4 | semidirect |
| 57. C2×D4×C197 | C2×C4 | semidirect |
| 64. C4⋊C4×C197 | D4 | semidirect |
| 130. C2×D197 | #102 | semidirect |
| 148. C197 | #1874 | semidirect |
| 153. C2×#102 | D197 | semidirect |
| 185. C2×D4 | C4×D197 | semidirect |
| 212. C4⋊C4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263297 | 2 |
| C2×C4⋊C4×D197 | 2 |
| C2×#20263247 | 2 |
| C2×#20263238 | 2 |
| #27160842 | 2 |
| #27160841 | 2 |
| C2×#102×C197 | 2 |
| #1874 | 197 |