Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1234 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1234 conjugacy classes of subgroups — too many to draw. Only its 224 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. D53⋊#432 | C2 | semidirect |
| 2. #20290196 | C2 | semidirect |
| 3. #20290186 | C2 | semidirect |
| 6. #16811645 | C22 | semidirect |
| 11. #16811582 | C22 | semidirect |
| 12. #16811479 | C22 | semidirect |
| 195. C53 | #17675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#432 | 2 |
| #20290196 | 2 |
| #20290186 | 2 |
| C2×#16811174 | 2 |
| #17675 | 53 |