Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
770 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20285702 | C2 | semidirect |
| 2. #20285165 | C2 | semidirect |
| 3. #20273429 | C2 | semidirect |
| 4. #20273313 | C2 | semidirect |
| 5. #20273222 | C2 | semidirect |
| 6. #20272608 | C2 | semidirect |
| 7. C53×#2657 | C2 | semidirect |
| 38. #13133217 | D4 | semidirect |
| 39. #13133214 | D4 | semidirect |
| 46. C4⋊#88322 | D4 | semidirect |
| 53. #13133128 | D4 | semidirect |
| 207. #2657 | D53 | semidirect |
| 242. C53 | #10088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285702 | 2 |
| #20285165 | 2 |
| #20273429 | 2 |
| #20273313 | 2 |
| #20273222 | 2 |
| #20272608 | 2 |
| C53×#2657 | 2 |
| #10088 | 53 |