Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 10. #16811512 | C4 | semidirect |
| 11. #16811511 | C4 | semidirect |
| 14. #16810399 | C4 | semidirect |
| 15. #16810398 | C4 | semidirect |
| 16. C53×#346 | C4 | semidirect |
| 100. #346 | #6157 | semidirect |
| 101. C53 | #12591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290916 | 2 |
| C4×C8×#6157 | 2 |
| (C2×#6157)⋊C16 | 2 |
| #346×D53 | 2 |
| #12591 | 53 |