Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 4. C2×#13133284 | C4 | semidirect |
| 8. C2×C4×#88324 | C4 | semidirect |
| 10. #16811501 | C4 | semidirect |
| 14. #16810390 | C4 | semidirect |
| 15. C53×#342 | C4 | semidirect |
| 189. #342 | #6157 | semidirect |
| 190. C53 | #7237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290838 | 2 |
| #20290577 | 2 |
| #20274702 | 2 |
| #7237 | 53 |