Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
630 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 112 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. #20290378 | C2 | semidirect |
| 2. C2×#16811489 | C2 | semidirect |
| 3. #20289534 | C2 | semidirect |
| 4. #20289531 | C2 | semidirect |
| 229. C53 | #7678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290378 | 2 |
| C2×#16811489 | 2 |
| #20289534 | 2 |
| #20289531 | 2 |
| #20283041 | 2 |
| #7678 | 53 |