Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 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 |
|---|---|---|
| 1. C2×#20263346 | C2 | semidirect |
| 2. #27161629 | C2 | semidirect |
| 3. #27161461 | C2 | semidirect |
| 4. #27161458 | C2 | semidirect |
| 5. #27161455 | C2 | semidirect |
| 6. #27161453 | C2 | semidirect |
| 7. #27161451 | C2 | semidirect |
| 8. C2×C4×#13096802 | C2 | semidirect |
| 9. #532×C197 | C2 | semidirect |
| 42. C2×#13096802 | D4 | semidirect |
| 93. C4×C197 | #135 | semidirect |
| 101. C197 | #3147 | semidirect |
| 105. #532 | D197 | semidirect |
| 196. C4 | #20263346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| #27161629 | 2 |
| #27161461 | 2 |
| #27161458 | 2 |
| #27161455 | 2 |
| #27161453 | 2 |
| #27161451 | 2 |
| C2×C4×#13096802 | 2 |
| #532×C197 | 2 |
| #3147 | 197 |