Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20276434 | C2 | semidirect |
| 4. #20272820 | C2 | semidirect |
| 10. #16810881 | C4 | semidirect |
| 24. C2×Dic212 | C2×C4 | semidirect |
| 34. #13133149 | C2×C4 | semidirect |
| 167. C53 | #13000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810881 | 2 |
| #20276434 | 2 |
| C2×#16810405 | 2 |
| #20272820 | 2 |
| C53×#2911 | 2 |
| #13000 | 53 |