Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16810456 | C2 | semidirect |
| 3. #366×D53 | C2 | semidirect |
| 4. #20272897 | C2 | semidirect |
| 5. #20272895 | C2 | semidirect |
| 6. #20272893 | C2 | semidirect |
| 7. C53×#1415 | C2 | semidirect |
| 10. #16811052 | C4 | semidirect |
| 30. Dic424 | C2×C4 | semidirect |
| 40. D16×C53 | C2×C4 | semidirect |
| 106. #1415 | D53 | semidirect |
| 126. C53 | #13616 | semidirect |
| 139. D16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811052 | 2 |
| C2×#16810456 | 2 |
| #366×D53 | 2 |
| #20272897 | 2 |
| #20272895 | 2 |
| #20272893 | 2 |
| C53×#1415 | 2 |
| #13616 | 53 |