Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×D424 | C2 | semidirect |
| 2. #20276939 | C2 | semidirect |
| 4. #20274075 | C2 | semidirect |
| 5. #20272769 | C2 | semidirect |
| 6. #20272677 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 83. D424 | SD16 | semidirect |
| 89. Q8×C53 | D16 | semidirect |
| 137. Q8⋊C16 | D53 | semidirect |
| 161. C53 | #12352 | semidirect |
| 229. Q8 | D848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D424 | 2 |
| #20276939 | 2 |
| #20276751 | 2 |
| #20274075 | 2 |
| #20272769 | 2 |
| #20272677 | 2 |
| C53×Q8⋊C16 | 2 |
| #12352 | 53 |