Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
676 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×Q8⋊#88322 | C2 | semidirect |
| 4. #20272598 | C2 | semidirect |
| 5. C53×#2582 | C2 | semidirect |
| 55. C2×Q8×C53 | SD16 | semidirect |
| 148. #2582 | D53 | semidirect |
| 172. C53 | #10230 | semidirect |
| 208. C2×Q8 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810823 | 2 |
| #20275520 | 2 |
| C2×Q8⋊#88322 | 2 |
| #20272598 | 2 |
| C53×#2582 | 2 |
| #10230 | 53 |