Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291461 | C2 | semidirect |
| 2. #20290878 | C2 | semidirect |
| 3. #20290096 | C2 | semidirect |
| 4. #20290022 | C2 | semidirect |
| 5. #20289550 | C2 | semidirect |
| 6. #20289547 | C2 | semidirect |
| 24. #16811000 | C4 | semidirect |
| 25. #16810971 | C4 | semidirect |
| 26. #16810971 | C4 | semidirect |
| 30. C53×#500 | C4 | semidirect |
| 115. #11719936 | D8 | semidirect |
| 226. #500 | #6157 | semidirect |
| 246. C53 | #9053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291461 | 2 |
| #20290878 | 2 |
| #20290096 | 2 |
| #20290022 | 2 |
| #20289550 | 2 |
| #20289547 | 2 |
| #20285295 | 2 |
| #9053 | 53 |