Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #20272695 | C2 | semidirect |
| 5. Q8⋊#11719908 | C2 | semidirect |
| 6. #20272693 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 148. Q8⋊C16 | D53 | semidirect |
| 172. C53 | #11640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283644 | 2 |
| #20276517 | 2 |
| #20276512 | 2 |
| #20272695 | 2 |
| Q8⋊#11719908 | 2 |
| #20272693 | 2 |
| C53×Q8⋊C16 | 2 |
| #11640 | 53 |