Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#20263271 | C2 | semidirect |
| 2. #27161320 | C2 | semidirect |
| 4. #27160907 | C2 | semidirect |
| 5. #27160884 | C2 | semidirect |
| 6. #27160881 | C2 | semidirect |
| 7. C22×C16×C197 | C2 | semidirect |
| 39. C16×C197 | D4 | semidirect |
| 59. C22×C197 | SD32 | semidirect |
| 75. C197 | #2217 | semidirect |
| 78. C22×C16 | D197 | semidirect |
| 115. C16 | C22⋊D197 | semidirect |
| 138. C22 | #20263271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263271 | 2 |
| #27161320 | 2 |
| #27161315 | 2 |
| #27160907 | 2 |
| #27160884 | 2 |
| #27160881 | 2 |
| C22×C16×C197 | 2 |
| #2217 | 197 |