Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
622 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 3. #20276509 | C2 | semidirect |
| 4. C2×#16810452 | C2 | semidirect |
| 92. C53 | #33414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811040 | 2 |
| #20283326 | 2 |
| #20276509 | 2 |
| C2×#16810452 | 2 |
| C53×#2916 | 2 |
| #33414 | 53 |