Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
706 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 219 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. #20274332 | C2 | semidirect |
| 4. #20274324 | C2 | semidirect |
| 5. #20274310 | C2 | semidirect |
| 60. C2×C8×C53 | Q16 | semidirect |
| 136. C53 | #19604 | semidirect |
| 172. C2×C8 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285297 | 2 |
| #20285229 | 2 |
| #20274332 | 2 |
| #20274324 | 2 |
| #20274310 | 2 |
| C2×C8×#88322 | 2 |
| C53×#3160 | 2 |
| #19604 | 53 |