Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 2. C2×#16810734 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. #20275609 | C2 | semidirect |
| 5. #20272813 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C2×C53×#360 | C2 | semidirect |
| 12. C2×#13133160 | C4 | semidirect |
| 13. C2×#13133158 | C4 | semidirect |
| 45. C2×#11719908 | C2×C4 | semidirect |
| 58. C2×Q16×C53 | C2×C4 | semidirect |
| 60. C2×D8×C53 | C2×C4 | semidirect |
| 176. C2×#360 | D53 | semidirect |
| 205. C53 | #13037 | semidirect |
| 213. C2×Q16 | C4×D53 | semidirect |
| 221. C2×D8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| C2×#16810734 | 2 |
| C2×#16810437 | 2 |
| #20275609 | 2 |
| #20272813 | 2 |
| #20272794 | 2 |
| C2×C53×#360 | 2 |
| #13037 | 53 |