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 |
|---|---|---|
| 2. C4×D848 | C2 | semidirect |
| 3. #20272915 | C2 | semidirect |
| 4. #20272894 | C2 | semidirect |
| 5. C4×C32×C53 | C2 | semidirect |
| 8. D1696 | C4 | direct (N × H) |
| 17. D848 | C2×C4 | semidirect |
| 24. C32×C53 | C2×C4 | semidirect |
| 54. C4×C53 | D32 | semidirect |
| 62. C4×C32 | D53 | semidirect |
| 75. C53 | C4×D32 | semidirect |
| 86. C32 | C4×D53 | semidirect |
| 116. C4 | D1696 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1696 | 2 |
| C4×D848 | 2 |
| #20272915 | 2 |
| #20272894 | 2 |
| C4×C32×C53 | 2 |
| C4×D32 | 53 |