Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 7. #16811552 | C4 | direct (N × H) |
| 78. C4×C53 | #368 | semidirect |
| 82. Dic53 | #368 | semidirect |
| 103. C53 | C4×#368 | semidirect |
| 168. C4 | #16811552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811552 | 2 |
| C4×#13133288 | 2 |
| #20289775 | 2 |
| C4×C16×D53 | 2 |
| C4×#368 | 53 |