Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1526 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1526 conjugacy classes of subgroups — too many to draw. Only its 299 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 |
|---|---|---|
| 1. C2×#16811008 | C2 | semidirect |
| 3. C2×#16810997 | C2 | semidirect |
| 4. #20283073 | C2 | semidirect |
| 5. C4×C8×Dic53 | C2 | semidirect |
| 6. C2×C53×#494 | C2 | semidirect |
| 36. C8×Dic53 | D4 | semidirect |
| 100. C4×C53 | #495 | semidirect |
| 105. C2×#494 | D53 | semidirect |
| 129. C53 | #33303 | semidirect |
| 208. C4 | #16811008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811008 | 2 |
| C2×#16811000 | 2 |
| C2×#16810997 | 2 |
| #20283073 | 2 |
| C4×C8×Dic53 | 2 |
| C2×C53×#494 | 2 |
| #33303 | 53 |