Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×#16811548 | C2 | semidirect |
| 2. C2×#16811547 | C2 | semidirect |
| 5. #20289780 | C2 | semidirect |
| 6. #20289780 | C2 | semidirect |
| 19. C2×#13133157 | C4 | semidirect |
| 24. C2×C16×D53 | C4 | semidirect |
| 25. C2×C16×D53 | C4 | semidirect |
| 26. C2×M32×C53 | C4 | semidirect |
| 109. C16×C53 | C22⋊C4 | semidirect |
| 111. #11719908 | C22⋊C4 | semidirect |
| 162. C2×D53 | #365 | semidirect |
| 193. C2×M32 | #6157 | semidirect |
| 206. C53 | #12831 | semidirect |
| 291. C16 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811548 | 2 |
| C2×#16811547 | 2 |
| #20290594 | 2 |
| #20290591 | 2 |
| #20289780 | 2 |
| C2×M32×D53 | 2 |
| #12831 | 53 |