Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276488 | C2 | semidirect |
| 5. #20275505 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C53×#2151 | C2 | semidirect |
| 133. #2151 | D53 | semidirect |
| 159. C53 | #13468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276488 | 2 |
| #20276444 | 2 |
| C2×#16810431 | 2 |
| #20275613 | 2 |
| #20275505 | 2 |
| #20272811 | 2 |
| C53×#2151 | 2 |
| #13468 | 53 |