Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#16810367 | C2 | semidirect |
| 3. #20272860 | C2 | direct (N × H) |
| 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 |
| 200. C2×C53 | #1402 | semidirect |
| 202. C2×H(5,𝔽2) | Dic53 | semidirect |
| 207. #453 | Dic53 | semidirect |
| 211. C2×#100 | Dic53 | semidirect |
| 217. C53 | C2×#1402 | semidirect |
| 221. H(5,𝔽2) | C2×Dic53 | semidirect |
| 248. #100 | C2×Dic53 | semidirect |
| 393. C2 | #20272860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| C2×#16810367 | 2 |
| #20272860 | 2 |
| C2×C53×#453 | 2 |
| C2×#1402 | 53 |