Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16810435 | C2 | semidirect |
| 3. #20276430 | C2 | semidirect |
| 4. #20272797 | C2 | semidirect |
| 5. C53×#1945 | C2 | semidirect |
| 40. #107×C53 | D4 | semidirect |
| 117. #1945 | D53 | semidirect |
| 136. C53 | #13413 | semidirect |
| 159. #107 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810435 | 2 |
| #20276430 | 2 |
| #20272797 | 2 |
| C53×#1945 | 2 |
| #13413 | 53 |