Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
| 3. C2×#16810445 | C2 | semidirect |
| 6. #20272815 | C2 | semidirect |
| 7. C53×#1383 | C2 | semidirect |
| 19. #16810402 | C4 | semidirect |
| 146. #1383 | D53 | semidirect |
| 168. C53 | #12930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810658 | 2 |
| C2×#16810446 | 2 |
| C2×#16810445 | 2 |
| #20276325 | 2 |
| #20274750 | 2 |
| #20272815 | 2 |
| C53×#1383 | 2 |
| #12930 | 53 |