Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 203 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. #20276992 | C2 | direct (N × H) |
| 96. C2×C53 | #2253 | semidirect |
| 113. C53 | C2×#2253 | semidirect |
| 183. C2 | #20276992 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811024 | 2 |
| #20276992 | 2 |
| C2×#16810450 | 2 |
| C2×#16810449 | 2 |
| C2×C16×Dic53 | 2 |
| C2×C53×#366 | 2 |
| C2×#2253 | 53 |