Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
296 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 13. #20263255 | C4 | semidirect |
| 15. C8×Dic197 | C4 | semidirect |
| 30. #15691337 | C8 | direct (N × H) |
| 65. C8×C197 | C4⋊C4 | semidirect |
| 78. Dic197 | C4×C8 | semidirect |
| 84. C197 | C8×C4⋊C4 | semidirect |
| 150. C8 | #15691337 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263255 | 2 |
| C2×C8×Dic197 | 2 |
| C4×#15691337 | 2 |
| #27160834 | 2 |
| #27160833 | 2 |
| C2×C4×C8×C197 | 2 |
| C8×C4⋊C4 | 197 |