Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16810746 | C2 | semidirect |
| 3. #20276465 | C2 | semidirect |
| 4. #20276444 | C2 | semidirect |
| 5. #20275608 | C2 | semidirect |
| 6. #20272827 | C2 | semidirect |
| 7. C53×#1377 | C2 | semidirect |
| 12. #16811066 | C4 | semidirect |
| 14. #16811061 | C4 | semidirect |
| 182. #1377 | D53 | semidirect |
| 210. C53 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| C2×#16810746 | 2 |
| #20276465 | 2 |
| #20276444 | 2 |
| #20275608 | 2 |
| #20272827 | 2 |
| C53×#1377 | 2 |
| #13024 | 53 |