Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 128 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. #20289754 | C2 | semidirect |
| 3. #20289753 | C2 | semidirect |
| 132. C53 | #12845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811518 | 2 |
| #20289754 | 2 |
| #20289753 | 2 |
| C2×#16810580 | 2 |
| #12845 | 53 |