Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 4. #20276966 | C2 | direct (N × H) |
| 92. C2×Dic53 | Q32 | semidirect |
| 110. Dic53 | C2×Q32 | semidirect |
| 117. C2×C53 | #2247 | semidirect |
| 136. C53 | C2×#2247 | semidirect |
| 224. C2 | #20276966 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic424 | 2 |
| C22×#13133163 | 2 |
| C2×#16811001 | 2 |
| #20276966 | 2 |
| C2×C16×Dic53 | 2 |
| C22×Q32×C53 | 2 |
| C2×#2247 | 53 |