Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276791 | C2 | semidirect |
| 2. #20274329 | C2 | semidirect |
| 3. #20272752 | C2 | semidirect |
| 4. #20272688 | C2 | semidirect |
| 5. C53×#3292 | C2 | semidirect |
| 7. #16811000 | C22 | semidirect |
| 9. #16810444 | C22 | semidirect |
| 11. C8×#88322 | C22 | semidirect |
| 45. Q16×C53 | D8 | semidirect |
| 51. D8×C53 | D8 | semidirect |
| 92. #3292 | D53 | semidirect |
| 113. C53 | #12310 | semidirect |
| 142. Q16 | #11719922 | semidirect |
| 151. D8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276791 | 2 |
| #20274329 | 2 |
| #20272752 | 2 |
| #20272688 | 2 |
| C53×#3292 | 2 |
| #12310 | 53 |