Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 94 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. #20290908 | C2 | semidirect |
| 3. #20290230 | C2 | semidirect |
| 5. #20289585 | C2 | semidirect |
| 6. #20289560 | C2 | semidirect |
| 258. C53 | #9249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11719940 | 2 |
| #20290908 | 2 |
| #20290230 | 2 |
| #20290040 | 2 |
| #20289585 | 2 |
| #20289560 | 2 |
| C2×#16810911 | 2 |
| #9249 | 53 |