Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 1. #20286164 | C2 | semidirect |
| 5. #20272732 | C2 | semidirect |
| 6. #20272656 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 161. #1350 | D53 | semidirect |
| 187. C53 | #12165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286164 | 2 |
| #20276646 | 2 |
| #20276643 | 2 |
| #20275972 | 2 |
| #20272732 | 2 |
| #20272656 | 2 |
| C53×#1350 | 2 |
| #12165 | 53 |