Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
594 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. C2×#16811001 | C2 | semidirect |
| 4. C2×#16810426 | C2 | semidirect |
| 6. #20272792 | C2 | semidirect |
| 7. C2×C53×#358 | C2 | semidirect |
| 154. C2×Dic53 | SD32 | semidirect |
| 191. C2×#358 | D53 | semidirect |
| 221. C53 | #13327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| C22×#13133160 | 2 |
| C2×#16811001 | 2 |
| C2×#16810426 | 2 |
| #20275579 | 2 |
| #20272792 | 2 |
| C2×C53×#358 | 2 |
| #13327 | 53 |