Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20273629 | C2 | semidirect |
| 2. #20273539 | C2 | semidirect |
| 3. #20272781 | C2 | semidirect |
| 4. #20272682 | C2 | semidirect |
| 5. #20272682 | C2 | semidirect |
| 6. #20272637 | C2 | semidirect |
| 51. D8×C53 | M16 | semidirect |
| 131. C53 | #12078 | semidirect |
| 160. D8 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273629 | 2 |
| #20273539 | 2 |
| #20272781 | 2 |
| #20272682 | 2 |
| #20272637 | 2 |
| C53×#2177 | 2 |
| #12078 | 53 |