Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 75 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. D16×Dic53 | C2 | semidirect |
| 2. #20272915 | C2 | semidirect |
| 3. #20272893 | C2 | semidirect |
| 4. C32×Dic53 | C2 | semidirect |
| 12. C53×D32 | C4 | semidirect |
| 22. D16×C53 | C2×C4 | semidirect |
| 24. C32×C53 | C2×C4 | semidirect |
| 57. Dic53 | D32 | direct (N × H) |
| 69. D32 | Dic53 | direct (N × H) |
| 75. C53 | C4×D32 | semidirect |
| 79. D16 | C2×Dic53 | semidirect |
| 86. C32 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×Dic53 | 2 |
| #20272915 | 2 |
| #20272893 | 2 |
| C32×Dic53 | 2 |
| C2×C53×D32 | 2 |
| C4×D32 | 53 |