Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20283567 | C2 | semidirect |
| 2. C2×#16810436 | C2 | semidirect |
| 3. #20276431 | C2 | semidirect |
| 4. #20275626 | C2 | semidirect |
| 5. #20272811 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 24. C2×D16×C53 | C4 | semidirect |
| 56. C2×D8×C53 | C2×C4 | semidirect |
| 63. C2×C16×C53 | C2×C4 | semidirect |
| 178. C2×D16 | Dic53 | semidirect |
| 191. C53 | #13017 | semidirect |
| 203. C2×D8 | C2×Dic53 | semidirect |
| 220. C2×C16 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283567 | 2 |
| C2×#16810436 | 2 |
| #20276431 | 2 |
| #20275626 | 2 |
| #20272811 | 2 |
| #20272803 | 2 |
| C22×D16×C53 | 2 |
| #13017 | 53 |