Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20277889 | C2 | semidirect |
| 2. #20275540 | C2 | semidirect |
| 3. C2×#16810363 | C2 | semidirect |
| 4. #20272597 | C2 | semidirect |
| 20. C53×#496 | C4 | semidirect |
| 50. #127×C53 | C2×C4 | semidirect |
| 57. #97×C53 | C2×C4 | semidirect |
| 189. #496 | Dic53 | semidirect |
| 200. C53 | #9001 | semidirect |
| 216. #127 | C2×Dic53 | semidirect |
| 233. #97 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277889 | 2 |
| #20275540 | 2 |
| C2×#16810363 | 2 |
| #20272597 | 2 |
| C2×C53×#496 | 2 |
| #9001 | 53 |