Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1766 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1766 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20274630 | C2 | semidirect |
| 5. C2×#13133132 | C22 | semidirect |
| 9. C23×D4×C53 | C4 | semidirect |
| 13. C2×#127×C53 | C4 | semidirect |
| 15. C22×C42×C53 | C4 | semidirect |
| 80. C2×D4×C53 | C22⋊C4 | semidirect |
| 93. C42×C53 | C22⋊C4 | semidirect |
| 164. C22×C53 | #353 | semidirect |
| 184. C23×D4 | Dic53 | semidirect |
| 188. C2×#127 | Dic53 | semidirect |
| 190. C22×C42 | Dic53 | semidirect |
| 195. C53 | #12693 | semidirect |
| 260. C2×D4 | C22⋊Dic53 | semidirect |
| 276. C42 | C22⋊Dic53 | semidirect |
| 343. C22 | #16810416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| #20274630 | 2 |
| C22×#127×C53 | 2 |
| #12693 | 53 |