Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #20272754 | C2 | direct (N × H) |
| 87. C2×C53 | #1358 | semidirect |
| 98. C53 | C2×#1358 | semidirect |
| 169. C2 | #20272754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810444 | 2 |
| #20272754 | 2 |
| C2×C53×#494 | 2 |
| C2×#1358 | 53 |