Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #20276648 | C2 | semidirect |
| 4. #20275984 | C2 | semidirect |
| 6. #20272656 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 159. #1350 | D53 | semidirect |
| 186. C53 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286177 | 2 |
| #20276648 | 2 |
| #20276634 | 2 |
| #20275984 | 2 |
| #20272729 | 2 |
| #20272656 | 2 |
| C53×#1350 | 2 |
| #12169 | 53 |