Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #20272889 | C2 | semidirect |
| 4. #20272874 | C2 | semidirect |
| 6. #16811235 | C4 | semidirect |
| 8. #16810995 | C4 | semidirect |
| 9. #16810987 | C4 | semidirect |
| 15. #16810684 | C4 | semidirect |
| 28. #13133217 | C2×C4 | semidirect |
| 30. #13133209 | C2×C4 | semidirect |
| 42. #13133128 | C2×C4 | semidirect |
| 43. C4×#88322 | C2×C4 | semidirect |
| 175. C53 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285787 | 2 |
| #20276407 | 2 |
| #20272889 | 2 |
| #20272874 | 2 |
| C53×#2127 | 2 |
| #13607 | 53 |