Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C22×Dic788 | C2 | semidirect |
| 2. C2×Q16×D197 | C2 | semidirect |
| 4. #27161457 | C2 | semidirect |
| 5. #27161321 | C2 | semidirect |
| 6. #27161288 | C2 | semidirect |
| 7. #27161236 | C2 | semidirect |
| 8. #27161234 | C2 | semidirect |
| 9. #27161173 | C2 | semidirect |
| 11. #467×C197 | C2 | semidirect |
| 55. Dic788 | D4 | semidirect |
| 87. C22⋊D197 | Q16 | semidirect |
| 112. C22×C197 | C2×Q16 | semidirect |
| 116. C2×D197 | C2×Q16 | semidirect |
| 126. Dic197 | C2×Q16 | semidirect |
| 132. C197 | D4×Q16 | semidirect |
| 139. #467 | D197 | semidirect |
| 248. C22 | Q16×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic788 | 2 |
| C2×Q16×D197 | 2 |
| #27161742 | 2 |
| #27161457 | 2 |
| #27161321 | 2 |
| #27161288 | 2 |
| #27161236 | 2 |
| #27161234 | 2 |
| #27161173 | 2 |
| C8×C22⋊D197 | 2 |
| #467×C197 | 2 |
| D4×Q16 | 197 |