Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
594 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#16811003 | C2 | semidirect |
| 3. C2×#16810428 | C2 | semidirect |
| 5. C53×#1374 | C2 | semidirect |
| 96. C2×C4×C53 | SD32 | semidirect |
| 141. #1374 | D53 | semidirect |
| 162. C53 | #13327 | semidirect |
| 252. C2×C4 | #13133162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133162 | 2 |
| C2×#16811003 | 2 |
| C2×#16810428 | 2 |
| #20275581 | 2 |
| C53×#1374 | 2 |
| #13327 | 53 |