Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
850 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 1. #20274832 | C2 | semidirect |
| 2. #20274568 | C2 | semidirect |
| 3. C2×#16810367 | C2 | semidirect |
| 21. C4⋊#88322 | D4 | semidirect |
| 143. C53 | #9706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274832 | 2 |
| #20274568 | 2 |
| C2×#16810367 | 2 |
| C53×#2867 | 2 |
| #9706 | 53 |