Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#16811003 | C2 | semidirect |
| 3. C2×#16810370 | C2 | semidirect |
| 4. #20272550 | C2 | semidirect |
| 50. C2×D4×C53 | Q16 | semidirect |
| 155. C53 | #10274 | semidirect |
| 191. C2×D4 | Dic212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811003 | 2 |
| C2×#16810903 | 2 |
| C2×#16810370 | 2 |
| #20272550 | 2 |
| C53×#1954 | 2 |
| #10274 | 53 |