Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1506 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 246 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. C22×#13133305 | C2 | semidirect |
| 2. C2×#16811651 | C2 | semidirect |
| 3. #20290695 | C2 | semidirect |
| 4. #20290661 | C2 | semidirect |
| 5. #20290540 | C2 | semidirect |
| 6. #20290449 | C2 | semidirect |
| 31. C2×D53⋊C8 | D4 | semidirect |
| 101. C22×D53 | #131 | semidirect |
| 108. C2×C4×C53 | #131 | semidirect |
| 172. C53 | #21442 | semidirect |
| 266. C2×C4 | #13133305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133305 | 2 |
| C2×#16811651 | 2 |
| #20290695 | 2 |
| #20290661 | 2 |
| #20290540 | 2 |
| #20290449 | 2 |
| #20277933 | 2 |
| #21442 | 53 |