Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20273228 | C2 | semidirect |
| 5. #20273226 | C2 | semidirect |
| 6. #20272609 | C2 | semidirect |
| 7. C53×#1300 | C2 | semidirect |
| 10. #16810983 | C4 | semidirect |
| 11. #16810983 | C4 | semidirect |
| 34. #13133217 | C2×C4 | semidirect |
| 35. #13133217 | C2×C4 | semidirect |
| 72. #97×C53 | C2×C4 | semidirect |
| 204. #1300 | D53 | semidirect |
| 234. C53 | #9439 | semidirect |
| 271. #97 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285102 | 2 |
| #20277825 | 2 |
| #20273338 | 2 |
| #20273228 | 2 |
| #20273226 | 2 |
| #20272609 | 2 |
| C53×#1300 | 2 |
| #9439 | 53 |