Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
670 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 3. #20276585 | C2 | direct (N × H) |
| 9. C2×Dic424 | C4 | semidirect |
| 32. Dic424 | C2×C4 | semidirect |
| 103. C2×C53 | #2176 | semidirect |
| 120. C53 | C2×#2176 | semidirect |
| 196. C2 | #20276585 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic424 | 2 |
| C2×#16810717 | 2 |
| #20276585 | 2 |
| C2×#16810426 | 2 |
| C2×#16810398 | 2 |
| C2×C53×#367 | 2 |
| C2×#2176 | 53 |