Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#20263349 | C2 | semidirect |
| 2. C2×#20263347 | C2 | semidirect |
| 3. C2×#20263345 | C2 | semidirect |
| 4. #27161628 | C2 | semidirect |
| 5. #27161463 | C2 | semidirect |
| 6. #27161461 | C2 | semidirect |
| 7. #27161457 | C2 | semidirect |
| 8. #27161454 | C2 | semidirect |
| 9. #27161450 | C2 | semidirect |
| 10. C4×C8×D197 | C2 | semidirect |
| 11. #495×C197 | C2 | semidirect |
| 62. C8×D197 | D4 | semidirect |
| 63. C8×D197 | D4 | semidirect |
| 119. Dic197 | #135 | semidirect |
| 125. C197 | #3147 | semidirect |
| 133. #495 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| C2×#20263347 | 2 |
| C2×#20263345 | 2 |
| #27161628 | 2 |
| #27161463 | 2 |
| #27161461 | 2 |
| #27161457 | 2 |
| #27161454 | 2 |
| #27161450 | 2 |
| C4×C8×D197 | 2 |
| #495×C197 | 2 |
| #3147 | 197 |