Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
210 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20272781 | C2 | semidirect |
| 5. #20272780 | C2 | semidirect |
| 6. #20272780 | C2 | semidirect |
| 7. C53×#1368 | C2 | semidirect |
| 103. #1368 | D53 | semidirect |
| 123. C53 | #12028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276516 | 2 |
| #20273475 | 2 |
| #334×D53 | 2 |
| #20272781 | 2 |
| #20272780 | 2 |
| C53×#1368 | 2 |
| #12028 | 53 |