Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#16811510 | C2 | semidirect |
| 4. #20290519 | C2 | semidirect |
| 5. #20289776 | C2 | semidirect |
| 6. #20289775 | C2 | semidirect |
| 11. #16811667 | C4 | semidirect |
| 17. #16811538 | C4 | semidirect |
| 23. #16810427 | C4 | semidirect |
| 24. #16810425 | C4 | semidirect |
| 25. #16810423 | C4 | semidirect |
| 26. C53×#358 | C4 | semidirect |
| 181. #358 | #6157 | semidirect |
| 186. C53 | #12642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811667 | 2 |
| C2×#16811538 | 2 |
| C2×#16811510 | 2 |
| #20290519 | 2 |
| #20289776 | 2 |
| #20289775 | 2 |
| #20276421 | 2 |
| #12642 | 53 |