Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276997 | C2 | semidirect |
| 5. #20272774 | C2 | semidirect |
| 6. #20272771 | C2 | semidirect |
| 7. C53×#1371 | C2 | semidirect |
| 64. C16×C53 | SD16 | semidirect |
| 103. #1371 | D53 | semidirect |
| 125. C53 | #12456 | semidirect |
| 168. C16 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276997 | 2 |
| #20276548 | 2 |
| #20274115 | 2 |
| #20274105 | 2 |
| #20272774 | 2 |
| #20272771 | 2 |
| C53×#1371 | 2 |
| #12456 | 53 |