Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
220 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20272783 | C2 | semidirect |
| 79. C53 | #12002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810444 | 2 |
| #20272783 | 2 |
| C4×M32×C53 | 2 |
| #12002 | 53 |