Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 24. #16810975 | C4 | semidirect |
| 25. #16810974 | C4 | semidirect |
| 26. #16810973 | C4 | semidirect |
| 30. C53×#487 | C4 | semidirect |
| 234. #487 | #6157 | semidirect |
| 250. C53 | #9065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291244 | 2 |
| #20290893 | 2 |
| D53⋊#332 | 2 |
| #20289550 | 2 |
| #487×D53 | 2 |
| #9065 | 53 |