Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1630 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 283 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 |
|---|---|---|
| 2. #20277369 | C2 | semidirect |
| 3. #20275123 | C2 | semidirect |
| 4. #20274996 | C2 | semidirect |
| 5. #20274663 | C2 | semidirect |
| 6. C4×#13133132 | C2 | semidirect |
| 7. C4×H(5,𝔽2)×C53 | C2 | semidirect |
| 9. C22×#11719921 | C22 | semidirect |
| 10. #16810810 | C4 | semidirect |
| 18. #16810495 | C22 | semidirect |
| 19. #16810478 | C22 | semidirect |
| 20. C4×C22⋊Dic53 | C22 | semidirect |
| 21. #16810390 | C22 | semidirect |
| 33. #13133185 | C2×C4 | semidirect |
| 45. #13133132 | C2×C4 | semidirect |
| 55. C23×C4×C53 | D4 | semidirect |
| 69. C2×C4⋊C4×C53 | D4 | semidirect |
| 72. C2×C22⋊C4×C53 | D4 | semidirect |
| 75. C2×C42×C53 | D4 | semidirect |
| 83. C23×D53 | C22×C4 | semidirect |
| 126. C22⋊Dic53 | C22×C4 | semidirect |
| 215. C4×H(5,𝔽2) | D53 | semidirect |
| 250. C53 | #21482 | semidirect |
| 260. C23×C4 | C22⋊D53 | semidirect |
| 277. C2×C4⋊C4 | C22⋊D53 | semidirect |
| 288. C2×C22⋊C4 | C22⋊D53 | semidirect |
| 292. C2×C42 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810810 | 2 |
| #20277369 | 2 |
| #20275123 | 2 |
| #20274996 | 2 |
| #20274663 | 2 |
| C4×#13133132 | 2 |
| C4×H(5,𝔽2)×C53 | 2 |
| #21482 | 53 |