Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20276512 | C2 | semidirect |
| 3. #20276469 | C2 | semidirect |
| 4. Q8⋊#11719908 | C2 | semidirect |
| 5. #20272671 | C2 | semidirect |
| 6. #20272669 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 105. Q8×C53 | M32 | semidirect |
| 117. D212 | M32 | semidirect |
| 157. Q8⋊C16 | D53 | semidirect |
| 184. C53 | #11623 | semidirect |
| 263. Q8 | #13133156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#11719949 | 2 |
| #20276512 | 2 |
| #20276469 | 2 |
| Q8⋊#11719908 | 2 |
| #20272671 | 2 |
| #20272669 | 2 |
| C53×Q8⋊C16 | 2 |
| #11623 | 53 |