Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20273486 | C2 | semidirect |
| 4. #20273399 | C2 | semidirect |
| 5. #20273395 | C2 | semidirect |
| 6. #20272611 | C2 | semidirect |
| 186. C53 | #10448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810903 | 2 |
| #20274707 | 2 |
| #20273486 | 2 |
| #20273399 | 2 |
| #20273395 | 2 |
| #20272611 | 2 |
| C53×#1478 | 2 |
| #10448 | 53 |