Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16810670 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. C2×#16810435 | C2 | semidirect |
| 5. C2×#16810404 | C2 | semidirect |
| 6. #20272813 | C2 | semidirect |
| 7. C53×#1383 | C2 | semidirect |
| 54. #13133153 | D4 | semidirect |
| 64. #108×C53 | D4 | semidirect |
| 179. #1383 | D53 | semidirect |
| 204. C53 | #13010 | semidirect |
| 242. #108 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810877 | 2 |
| C2×#16810670 | 2 |
| C2×#16810437 | 2 |
| C2×#16810435 | 2 |
| C2×#16810404 | 2 |
| #20272813 | 2 |
| C53×#1383 | 2 |
| #13010 | 53 |