Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16810463 | C2 | direct (N × H) |
| 8. #16810463 | C22 | direct (N × H) |
| 55. C22×C53 | Q64 | semidirect |
| 65. C2×C53 | C2×Q64 | semidirect |
| 76. C53 | C22×Q64 | semidirect |
| 117. C22 | #16810463 | direct (N × H) |
| 123. C2 | C2×#16810463 | 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 |
| C2×#16810463 | 2 |
| C22×#13133123 | 2 |
| C22×Q32×C53 | 2 |
| C22×Q64 | 53 |