Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 134 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. #16811550 | C4 | direct (N × H) |
| 12. C4×#11719908 | C4 | semidirect |
| 13. C16×Dic53 | C4 | semidirect |
| 14. C16×Dic53 | C4 | semidirect |
| 15. C4×C16×C53 | C4 | semidirect |
| 53. C16×C53 | C42 | semidirect |
| 55. #11719908 | C42 | semidirect |
| 82. C4×C53 | #367 | semidirect |
| 86. Dic53 | #367 | semidirect |
| 105. C4×C16 | #6157 | semidirect |
| 107. C53 | C4×#367 | semidirect |
| 147. C16 | C4×#6157 | semidirect |
| 176. C4 | #16811550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811550 | 2 |
| C4×#13133286 | 2 |
| #20289773 | 2 |
| C4×C16×D53 | 2 |
| C4×#367 | 53 |