Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1092 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20275556 | C2 | semidirect |
| 2. #20273450 | C2 | semidirect |
| 3. #20273307 | C2 | semidirect |
| 4. #20273154 | C2 | semidirect |
| 6. #16810647 | C22 | semidirect |
| 8. C4×#11719917 | C22 | semidirect |
| 134. Q8×C53 | #100 | semidirect |
| 150. D4×C53 | #100 | semidirect |
| 221. C53 | #8469 | semidirect |
| 331. Q8 | #13133134 | semidirect |
| 347. D4 | #13133134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275556 | 2 |
| #20273450 | 2 |
| #20273307 | 2 |
| #20273154 | 2 |
| C53×#3498 | 2 |
| #8469 | 53 |