Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1830 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1830 conjugacy classes of subgroups — too many to draw. Only its 667 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. #20280680 | C2 | direct (N × H) |
| 98. C2×C53 | #2645 | semidirect |
| 116. C53 | C2×#2645 | semidirect |
| 187. C2 | #20280680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280680 | 2 |
| C2×C53⋊#401 | 2 |
| C2×#16810564 | 2 |
| C2×#16810529 | 2 |
| C2×#16810521 | 2 |
| C2×C53×#376 | 2 |
| C2×#2645 | 53 |