Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 3. #20272820 | C2 | semidirect |
| 4. #20272799 | C2 | semidirect |
| 5. C53×#3162 | C2 | semidirect |
| 21. C2×D424 | Q8 | semidirect |
| 115. #3162 | D53 | semidirect |
| 136. C53 | #13367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276430 | 2 |
| #20275591 | 2 |
| #20272820 | 2 |
| #20272799 | 2 |
| C53×#3162 | 2 |
| #13367 | 53 |