Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 116 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. #20290019 | C2 | semidirect |
| 4. #20289959 | C2 | semidirect |
| 5. #20289555 | C2 | semidirect |
| 6. #20289541 | C2 | semidirect |
| 45. C2×#11719923 | C8 | semidirect |
| 89. C2×Dic106 | C2×C8 | semidirect |
| 115. C2×#88322 | C2×C8 | semidirect |
| 211. C53 | #9087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291562 | 2 |
| #20290019 | 2 |
| #20290014 | 2 |
| #20289959 | 2 |
| #20289555 | 2 |
| #20289541 | 2 |
| C2×#16810720 | 2 |
| #9087 | 53 |