Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #20291405 | C2 | semidirect |
| 2. #20290621 | C2 | semidirect |
| 5. #20289587 | C2 | semidirect |
| 6. #20289557 | C2 | semidirect |
| 28. C2×#13133151 | C4 | semidirect |
| 29. C2×#13133148 | C4 | semidirect |
| 30. C2×#13133138 | C4 | semidirect |
| 32. C2×#102×C53 | C4 | semidirect |
| 244. C2×#102 | #6157 | semidirect |
| 256. C53 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291405 | 2 |
| #20290621 | 2 |
| #20290111 | 2 |
| #20289990 | 2 |
| #20289587 | 2 |
| #20289557 | 2 |
| C2×#16810945 | 2 |
| #9242 | 53 |