Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 508 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×#16810746 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. C2×#16810432 | C2 | semidirect |
| 5. #20272813 | C2 | semidirect |
| 6. #20272795 | C2 | semidirect |
| 7. C53×#1972 | C2 | semidirect |
| 12. C2×#13133161 | C4 | semidirect |
| 13. C2×#13133158 | C4 | semidirect |
| 108. Dic212 | C22⋊C4 | semidirect |
| 110. D424 | C22⋊C4 | semidirect |
| 176. #1972 | D53 | semidirect |
| 204. C53 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811059 | 2 |
| C2×#16810746 | 2 |
| C2×#16810436 | 2 |
| C2×#16810432 | 2 |
| #20272813 | 2 |
| #20272795 | 2 |
| C53×#1972 | 2 |
| #13040 | 53 |