Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 1. C8×C4⋊#6157 | C2 | semidirect |
| 4. #20289929 | C2 | semidirect |
| 5. #20289611 | C2 | semidirect |
| 6. #20289605 | C2 | semidirect |
| 14. #16811482 | C4 | semidirect |
| 15. #16811481 | C4 | semidirect |
| 22. #16810702 | C4 | semidirect |
| 24. D4×#88322 | C4 | semidirect |
| 25. #16810688 | C4 | semidirect |
| 30. C53×#436 | C4 | semidirect |
| 212. #436 | #6157 | semidirect |
| 231. C53 | #8257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊#6157 | 2 |
| #20290212 | 2 |
| #20290094 | 2 |
| #20289929 | 2 |
| #20289611 | 2 |
| #20289605 | 2 |
| #20283424 | 2 |
| #8257 | 53 |