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. #20272695 | C2 | semidirect |
| 5. #20272693 | C2 | semidirect |
| 6. D4⋊#11719908 | C2 | semidirect |
| 7. C53×D4⋊C16 | C2 | semidirect |
| 105. D4×C53 | M32 | semidirect |
| 126. Dic106 | M32 | semidirect |
| 159. D4⋊C16 | D53 | semidirect |
| 184. C53 | #11623 | semidirect |
| 266. D4 | #13133156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#11719947 | 2 |
| #20276512 | 2 |
| #20276469 | 2 |
| #20272695 | 2 |
| #20272693 | 2 |
| D4⋊#11719908 | 2 |
| C53×D4⋊C16 | 2 |
| #11623 | 53 |