Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1318 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 191 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. C2×#16811235 | C2 | semidirect |
| 4. #20275862 | C2 | semidirect |
| 5. #20275800 | C2 | semidirect |
| 6. #20275069 | C2 | semidirect |
| 7. #20275025 | C2 | semidirect |
| 8. C53×#1818 | C2 | semidirect |
| 12. C2×#13133217 | C22 | semidirect |
| 14. C2×#13133209 | C22 | semidirect |
| 17. C2×C4×Dic106 | C22 | semidirect |
| 20. C2×#13133142 | C22 | semidirect |
| 26. #16810386 | C22 | semidirect |
| 29. C53×#336 | C22 | semidirect |
| 30. C53×#336 | C22 | semidirect |
| 188. #1818 | D53 | semidirect |
| 215. #336 | C2×D53 | semidirect |
| 216. #336 | C2×D53 | semidirect |
| 217. C53 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811235 | 2 |
| C2×#16810776 | 2 |
| #20277295 | 2 |
| #20275862 | 2 |
| #20275800 | 2 |
| #20275069 | 2 |
| #20275025 | 2 |
| C53×#1818 | 2 |
| #23942 | 53 |