Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2664 conjugacy classes of subgroups; only the 1093 normal subgroups are shown.
This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 1093 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. #20277889 | C2 | semidirect |
| 2. #20277856 | C2 | semidirect |
| 3. #124×Dic53 | C2 | semidirect |
| 4. #120×Dic53 | C2 | semidirect |
| 6. C24×Dic53 | C22 | semidirect |
| 7. C2×Q8×Dic53 | C22 | semidirect |
| 9. #16810530 | C22 | semidirect |
| 11. #16810516 | C22 | semidirect |
| 13. #16810498 | C22 | semidirect |
| 14. #16810489 | C22 | semidirect |
| 15. #16810479 | C22 | semidirect |
| 16. C22⋊C4×Dic53 | C22 | semidirect |
| 17. C42×Dic53 | C22 | semidirect |
| 18. C53×H(3,𝔽4) | C4 | semidirect |
| 36. #124×C53 | C2×C4 | semidirect |
| 37. #120×C53 | C2×C4 | semidirect |
| 42. C24×C53 | C22×C4 | semidirect |
| 46. C2×Q8×C53 | C22×C4 | semidirect |
| 57. C22⋊C4×C53 | C22×C4 | semidirect |
| 58. C42×C53 | C22×C4 | semidirect |
| 94. Dic53 | H(3,𝔽4) | direct (N × H) |
| 105. H(3,𝔽4) | Dic53 | direct (N × H) |
| 119. C53 | C4×H(3,𝔽4) | semidirect |
| 126. #124 | C2×Dic53 | semidirect |
| 127. #120 | C2×Dic53 | semidirect |
| 141. C24 | C22×Dic53 | semidirect |
| 145. C2×Q8 | C22×Dic53 | semidirect |
| 160. C22⋊C4 | C22×Dic53 | semidirect |
| 163. C42 | C22×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277889 | 2 |
| #20277856 | 2 |
| #124×Dic53 | 2 |
| #120×Dic53 | 2 |
| C2×C53×H(3,𝔽4) | 2 |
| C4×H(3,𝔽4) | 53 |