Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1156 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1156 conjugacy classes of subgroups — too many to draw. Only its 130 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. #20290607 | C2 | semidirect |
| 2. C2×#16811474 | C2 | semidirect |
| 3. #20289891 | C2 | semidirect |
| 14. C2×#13133217 | C4 | semidirect |
| 19. C2×D4×Dic53 | C4 | semidirect |
| 21. C2×#127×C53 | C4 | semidirect |
| 226. C2×#127 | #6157 | semidirect |
| 240. C53 | #8332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290607 | 2 |
| C2×#16811474 | 2 |
| #20289891 | 2 |
| C2×#16811171 | 2 |
| #8332 | 53 |