Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #20276435 | C2 | semidirect |
| 5. #20272812 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 7. C53×#1979 | C2 | semidirect |
| 12. C2×#13133160 | C4 | semidirect |
| 43. C2×#11719908 | C2×C4 | semidirect |
| 53. C2×Q16×C53 | C2×C4 | semidirect |
| 160. #1979 | D53 | semidirect |
| 186. C53 | #13019 | semidirect |
| 194. C2×Q16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133160 | 2 |
| #20283568 | 2 |
| C2×#16810435 | 2 |
| #20276435 | 2 |
| #20272812 | 2 |
| #20272804 | 2 |
| C53×#1979 | 2 |
| #13019 | 53 |