Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276939 | C2 | semidirect |
| 3. #20276863 | C2 | semidirect |
| 4. #20274119 | C2 | semidirect |
| 5. #20272762 | C2 | semidirect |
| 6. #20272677 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 136. Q8⋊C16 | D53 | semidirect |
| 160. C53 | #12384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287690 | 2 |
| #20276939 | 2 |
| #20276863 | 2 |
| #20274119 | 2 |
| #20272762 | 2 |
| #20272677 | 2 |
| C53×Q8⋊C16 | 2 |
| #12384 | 53 |