Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 144 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. C2×#16811516 | C2 | semidirect |
| 3. #20289757 | C2 | semidirect |
| 6. C22⋊#11719910 | C4 | semidirect |
| 18. C2×#11719910 | C2×C4 | semidirect |
| 106. C22×C53 | #347 | semidirect |
| 137. C53 | #12605 | semidirect |
| 227. C22 | #16811516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290942 | 2 |
| C2×#16811516 | 2 |
| #20289757 | 2 |
| C22×#13133127 | 2 |
| #12605 | 53 |