Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1318 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
| 3. #20275861 | C2 | semidirect |
| 4. #20275797 | C2 | semidirect |
| 5. #20275073 | C2 | semidirect |
| 6. #20275027 | C2 | semidirect |
| 7. #20274786 | C2 | semidirect |
| 11. C2×#13133217 | C22 | semidirect |
| 13. C2×#13133209 | C22 | semidirect |
| 16. C2×C4×Dic106 | C22 | semidirect |
| 18. C2×#13133140 | C22 | semidirect |
| 21. #16810385 | C22 | semidirect |
| 22. #16810378 | C22 | semidirect |
| 23. #16810378 | C22 | 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×#16810774 | 2 |
| #20275861 | 2 |
| #20275797 | 2 |
| #20275073 | 2 |
| #20275027 | 2 |
| #20274786 | 2 |
| C53×#2309 | 2 |
| #23942 | 53 |