Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 14. #16811483 | C4 | semidirect |
| 15. #16811482 | C4 | semidirect |
| 21. #16810754 | C4 | semidirect |
| 23. #16810750 | C4 | semidirect |
| 25. C8×Dic106 | C4 | semidirect |
| 30. C8×Q8×C53 | C4 | semidirect |
| 186. C8×Q8 | #6157 | semidirect |
| 203. C53 | #8254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290509 | 2 |
| #20290216 | 2 |
| #20290097 | 2 |
| #20289929 | 2 |
| #20289611 | 2 |
| #20289605 | 2 |
| #20283644 | 2 |
| #8254 | 53 |