Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
706 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 2. #20289539 | C2 | semidirect |
| 6. #16811640 | C4 | semidirect |
| 10. C4×#11719940 | C4 | semidirect |
| 24. C4×#88324 | C2×C4 | semidirect |
| 68. C42×C53 | M16 | semidirect |
| 78. C4×Dic53 | M16 | semidirect |
| 154. C53 | #7855 | semidirect |
| 218. C42 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291391 | 2 |
| #20289539 | 2 |
| C2×#16810469 | 2 |
| #7855 | 53 |