Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20287818 | C2 | semidirect |
| 3. #20276344 | C2 | semidirect |
| 4. #20272794 | C2 | semidirect |
| 5. C53×#2115 | C2 | semidirect |
| 39. C2×#11719908 | D4 | semidirect |
| 141. #2115 | D53 | semidirect |
| 163. C53 | #12988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287818 | 2 |
| #20283431 | 2 |
| #20276344 | 2 |
| #20272794 | 2 |
| C53×#2115 | 2 |
| #12988 | 53 |