Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16810446 | C2 | semidirect |
| 5. #20275443 | C2 | semidirect |
| 6. #20272814 | C2 | semidirect |
| 7. C53×#1376 | C2 | semidirect |
| 19. #16810434 | C4 | semidirect |
| 92. Dic212 | C4⋊C4 | semidirect |
| 94. D424 | C4⋊C4 | semidirect |
| 157. #1376 | D53 | semidirect |
| 180. C53 | #12950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810741 | 2 |
| C2×#16810446 | 2 |
| C2×#16810434 | 2 |
| #20275443 | 2 |
| #20272814 | 2 |
| C53×#1376 | 2 |
| #12950 | 53 |