Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20275468 | C2 | semidirect |
| 6. #20272821 | C2 | semidirect |
| 7. C53×#1375 | C2 | semidirect |
| 19. #16810425 | C4 | semidirect |
| 40. #13133151 | C2×C4 | semidirect |
| 54. C2×C16×C53 | C2×C4 | semidirect |
| 146. #1375 | D53 | semidirect |
| 168. C53 | #12956 | semidirect |
| 191. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810736 | 2 |
| C2×#16810446 | 2 |
| C2×#16810437 | 2 |
| #20276432 | 2 |
| #20275468 | 2 |
| #20272821 | 2 |
| C53×#1375 | 2 |
| #12956 | 53 |