Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 2. C2×#16810736 | C2 | semidirect |
| 3. C2×#16810435 | C2 | semidirect |
| 4. C2×#16810433 | C2 | semidirect |
| 5. #20272815 | C2 | semidirect |
| 6. #20272795 | C2 | semidirect |
| 7. C53×#1975 | C2 | semidirect |
| 12. C2×#13133160 | C4 | semidirect |
| 13. C2×#13133158 | C4 | semidirect |
| 46. C2×#11719908 | C2×C4 | semidirect |
| 55. C2×Q16×C53 | C2×C4 | semidirect |
| 57. C2×D8×C53 | C2×C4 | semidirect |
| 177. #1975 | 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×#16810736 | 2 |
| C2×#16810435 | 2 |
| C2×#16810433 | 2 |
| #20272815 | 2 |
| #20272795 | 2 |
| C53×#1975 | 2 |
| #13037 | 53 |