Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #27160906 | C2 | semidirect |
| 5. #27160905 | C2 | semidirect |
| 6. #27160904 | C2 | semidirect |
| 7. #367×C197 | C2 | semidirect |
| 11. #20263265 | C4 | semidirect |
| 30. #15691333 | C2×C4 | semidirect |
| 34. C16×C197 | C2×C4 | semidirect |
| 63. C197 | #2159 | semidirect |
| 69. #367 | D197 | semidirect |
| 98. C16 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263265 | 2 |
| #27161116 | 2 |
| #107×D197 | 2 |
| #27160906 | 2 |
| #27160905 | 2 |
| #27160904 | 2 |
| #367×C197 | 2 |
| #2159 | 197 |