Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27161552 | C2 | semidirect |
| 3. C2×#20263241 | C2 | semidirect |
| 4. C2×#20263240 | C2 | semidirect |
| 5. #27160846 | C2 | semidirect |
| 6. #27160845 | C2 | semidirect |
| 7. C2×#99×C197 | C2 | semidirect |
| 9. #20263309 | C4 | semidirect |
| 12. #20263295 | C4 | semidirect |
| 47. C22⋊Dic197 | C2×C4 | semidirect |
| 48. C22⋊Dic197 | D4 | semidirect |
| 52. C24×C197 | C2×C4 | semidirect |
| 62. C22×C4×C197 | C2×C4 | semidirect |
| 66. C22⋊C4×C197 | D4 | semidirect |
| 148. C197 | #1913 | semidirect |
| 154. C2×#99 | D197 | semidirect |
| 177. C24 | C4×D197 | semidirect |
| 199. C22×C4 | C4×D197 | semidirect |
| 214. C22⋊C4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161638 | 2 |
| #27161552 | 2 |
| C2×#20263241 | 2 |
| C2×#20263240 | 2 |
| #27160846 | 2 |
| #27160845 | 2 |
| C2×#99×C197 | 2 |
| #1913 | 197 |