Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
694 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 163 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. #20275520 | C2 | semidirect |
| 3. #20275520 | C2 | semidirect |
| 4. C2×#16810345 | C2 | semidirect |
| 5. C53×#1834 | C2 | semidirect |
| 9. #16811000 | C4 | semidirect |
| 72. C2×#88322 | D8 | semidirect |
| 127. #1834 | D53 | semidirect |
| 147. C53 | #9832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| #20275520 | 2 |
| C2×#16810345 | 2 |
| C53×#1834 | 2 |
| #9832 | 53 |