Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 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×#16810446 | C2 | semidirect |
| 5. #20275495 | C2 | semidirect |
| 6. #20272827 | C2 | semidirect |
| 7. C53×#1378 | C2 | semidirect |
| 18. #16810440 | C4 | semidirect |
| 19. #16810437 | C4 | semidirect |
| 146. #1378 | D53 | semidirect |
| 169. C53 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283633 | 2 |
| C2×#16810446 | 2 |
| #20276465 | 2 |
| C2×#16810434 | 2 |
| #20275495 | 2 |
| #20272827 | 2 |
| C53×#1378 | 2 |
| #12952 | 53 |