Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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×C16×D53 | C2 | semidirect |
| 3. C2×#16810430 | C2 | semidirect |
| 4. #20274750 | C2 | semidirect |
| 5. #20272812 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C2×C53×#359 | C2 | semidirect |
| 44. C2×#11719908 | D4 | semidirect |
| 65. C2×C16×C53 | D4 | semidirect |
| 167. C2×D53 | #359 | semidirect |
| 178. C2×#359 | D53 | semidirect |
| 207. C53 | #13063 | semidirect |
| 239. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D53 | 2 |
| #20284292 | 2 |
| C2×#16810430 | 2 |
| #20274750 | 2 |
| #20272812 | 2 |
| #20272811 | 2 |
| C2×C53×#359 | 2 |
| #13063 | 53 |