Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
802 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 212 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. #20289537 | C2 | semidirect |
| 51. C2×#88324 | M16 | semidirect |
| 55. C2×C8×C53 | M16 | semidirect |
| 65. C2×#88322 | M16 | semidirect |
| 122. C53 | #7852 | semidirect |
| 167. C2×C8 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719936 | 2 |
| #20289537 | 2 |
| C2×#16810575 | 2 |
| #7852 | 53 |