Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
702 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 1. C4×C22⋊#88324 | C2 | semidirect |
| 2. #20290378 | C2 | semidirect |
| 3. #20289532 | C2 | semidirect |
| 4. #20289531 | C2 | semidirect |
| 251. C53 | #7684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊#88324 | 2 |
| #20290378 | 2 |
| #20289532 | 2 |
| #20289531 | 2 |
| #20283058 | 2 |
| #7684 | 53 |