Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4122 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 4122 conjugacy classes of subgroups — too many to draw. Only its 555 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×#13133132 | C2 | semidirect |
| 2. #20277293 | C2 | semidirect |
| 3. #20274663 | C2 | semidirect |
| 5. C22×C22⋊Dic53 | C22 | semidirect |
| 6. C22×C22⋊Dic53 | C22 | semidirect |
| 8. C2×#13133132 | C22 | semidirect |
| 10. #16810503 | C22 | semidirect |
| 15. C2×H(5,𝔽2)×C53 | C4 | semidirect |
| 21. C23×Dic53 | C23 | semidirect |
| 27. C2×C22⋊Dic53 | C23 | semidirect |
| 36. H(5,𝔽2)×C53 | C2×C4 | semidirect |
| 64. C24×C53 | C22⋊C4 | semidirect |
| 89. C2×D4×C53 | C22⋊C4 | semidirect |
| 97. C22×C4×C53 | C22⋊C4 | semidirect |
| 190. C2×H(5,𝔽2) | Dic53 | semidirect |
| 203. C53 | #20609 | semidirect |
| 210. H(5,𝔽2) | C2×Dic53 | semidirect |
| 248. C24 | C22⋊Dic53 | semidirect |
| 273. C2×D4 | C22⋊Dic53 | semidirect |
| 286. C22×C4 | C22⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133132 | 2 |
| #20277293 | 2 |
| #20274663 | 2 |
| C22×H(5,𝔽2)×C53 | 2 |
| #20609 | 53 |