Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
178 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 8. #16811550 | C4 | semidirect |
| 9. #16811549 | C4 | semidirect |
| 11. #16810457 | C4 | semidirect |
| 14. C53×M64 | C4 | semidirect |
| 84. M64 | #6157 | semidirect |
| 90. C53 | #7477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291066 | 2 |
| C2×#16811550 | 2 |
| M64×D53 | 2 |
| #7477 | 53 |