Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. #27161495 | C2 | semidirect |
| 2. #27161351 | C2 | semidirect |
| 4. #27160909 | C2 | semidirect |
| 5. #27160895 | C2 | semidirect |
| 6. #27160892 | C2 | semidirect |
| 7. C2×SD32×C197 | C2 | semidirect |
| 71. C197 | #2223 | semidirect |
| 73. C2×SD32 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161495 | 2 |
| #27161351 | 2 |
| #27161346 | 2 |
| #27160909 | 2 |
| #27160895 | 2 |
| #27160892 | 2 |
| C2×SD32×C197 | 2 |
| #2223 | 197 |