Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161740 | C2 | semidirect |
| 3. #27161464 | C2 | semidirect |
| 4. #27161317 | C2 | semidirect |
| 5. #27161315 | C2 | semidirect |
| 6. #27161303 | C2 | semidirect |
| 7. #27161240 | C2 | semidirect |
| 8. #27161218 | C2 | semidirect |
| 9. Q16×Dic197 | C2 | semidirect |
| 10. C8×C22⋊D197 | C2 | semidirect |
| 11. C22×Q16×C197 | C2 | semidirect |
| 76. Q16×C197 | D4 | semidirect |
| 113. C22×C197 | #135 | semidirect |
| 136. C197 | #3285 | semidirect |
| 139. C22×Q16 | D197 | semidirect |
| 195. Q16 | C22⋊D197 | semidirect |
| 256. C22 | #20263349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| #27161740 | 2 |
| #27161464 | 2 |
| #27161317 | 2 |
| #27161315 | 2 |
| #27161303 | 2 |
| #27161240 | 2 |
| #27161218 | 2 |
| Q16×Dic197 | 2 |
| C8×C22⋊D197 | 2 |
| C22×Q16×C197 | 2 |
| #3285 | 197 |