Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 3. C2×#16811516 | C2 | semidirect |
| 4. #20289757 | C2 | semidirect |
| 7. C2×#13133291 | C4 | semidirect |
| 11. C22×#11719910 | C4 | semidirect |
| 12. C22⋊#11719910 | C4 | semidirect |
| 13. C22⋊#11719910 | C4 | semidirect |
| 77. #11719910 | C22⋊C4 | semidirect |
| 115. C22×C53 | #347 | semidirect |
| 149. C53 | #12616 | semidirect |
| 244. C22 | #16811516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133291 | 2 |
| #20290942 | 2 |
| C2×#16811516 | 2 |
| #20289757 | 2 |
| #20274494 | 2 |
| #12616 | 53 |