Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20291155 | C2 | semidirect |
| 4. #20290058 | C2 | semidirect |
| 5. #20289602 | C2 | semidirect |
| 6. #20289567 | C2 | semidirect |
| 25. #16810919 | C4 | semidirect |
| 26. #16810918 | C4 | semidirect |
| 27. #16810820 | C4 | semidirect |
| 32. C53×#460 | C4 | semidirect |
| 152. Q8×C53 | #104 | semidirect |
| 182. Dic106 | #104 | semidirect |
| 231. #460 | #6157 | semidirect |
| 249. C53 | #9326 | semidirect |
| 364. Q8 | #13133281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291155 | 2 |
| #20290879 | 2 |
| #20290104 | 2 |
| #20290058 | 2 |
| #20289602 | 2 |
| #20289567 | 2 |
| #20284836 | 2 |
| #9326 | 53 |