Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275631 | C2 | semidirect |
| 5. #20272810 | C2 | semidirect |
| 6. #20272805 | C2 | semidirect |
| 7. C53×#2141 | C2 | semidirect |
| 12. C2×#13133160 | C4 | semidirect |
| 42. C2×#11719908 | C2×C4 | semidirect |
| 56. C2×Q16×C53 | C2×C4 | semidirect |
| 159. #2141 | 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 |
| #20283566 | 2 |
| C2×#16810437 | 2 |
| #20275631 | 2 |
| #20272810 | 2 |
| #20272805 | 2 |
| C53×#2141 | 2 |
| #13019 | 53 |