Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20276943 | C2 | semidirect |
| 4. #20274085 | C2 | semidirect |
| 5. #20272769 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 87. Q8×C53 | SD32 | semidirect |
| 131. Q8⋊C16 | D53 | semidirect |
| 154. C53 | #12356 | semidirect |
| 222. Q8 | #13133162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D424 | 2 |
| #20276943 | 2 |
| #20276761 | 2 |
| #20274085 | 2 |
| #20272769 | 2 |
| #20272677 | 2 |
| C53×Q8⋊C16 | 2 |
| #12356 | 53 |