Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 86 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. C4×#13133286 | C2 | semidirect |
| 2. #20290278 | C2 | semidirect |
| 4. #20289567 | C2 | semidirect |
| 15. #16810750 | C4 | semidirect |
| 16. C8×Dic106 | C4 | semidirect |
| 17. #16810701 | C4 | semidirect |
| 24. C8×D4×C53 | C4 | semidirect |
| 168. C8×D4 | #6157 | semidirect |
| 181. C53 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133286 | 2 |
| #20290278 | 2 |
| #20290117 | 2 |
| #20289567 | 2 |
| #20283687 | 2 |
| #8697 | 53 |