Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
550 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 79 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×#16810416 | C2 | semidirect |
| 2. #20273429 | C2 | semidirect |
| 3. #20272860 | C2 | semidirect |
| 8. #16810416 | C22 | semidirect |
| 10. #16810367 | C22 | semidirect |
| 11. C2×H(5,𝔽2)×C53 | C4 | semidirect |
| 16. C53×#453 | C4 | semidirect |
| 19. C2×#100×C53 | C4 | semidirect |
| 29. H(5,𝔽2)×C53 | C2×C4 | semidirect |
| 52. #100×C53 | C2×C4 | semidirect |
| 196. C2×H(5,𝔽2) | Dic53 | semidirect |
| 201. #453 | Dic53 | semidirect |
| 205. C2×#100 | Dic53 | semidirect |
| 211. C53 | #13561 | semidirect |
| 215. H(5,𝔽2) | C2×Dic53 | semidirect |
| 240. #100 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| #20273429 | 2 |
| #20272860 | 2 |
| C2×C53×#453 | 2 |
| #13561 | 53 |