Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 627 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. #20282967 | C2 | direct (N × H) |
| 2. C2×#16810536 | C2 | semidirect |
| 3. C2×#16810535 | C2 | semidirect |
| 4. C2×#16810534 | C2 | semidirect |
| 6. C2×C53×#393 | C2 | semidirect |
| 8. C23×Dic106 | C22 | semidirect |
| 12. #16810536 | C22 | semidirect |
| 13. #16810535 | C22 | semidirect |
| 14. #16810534 | C22 | semidirect |
| 16. C2×#13133124 | C22 | semidirect |
| 17. C2×#13133124 | C22 | semidirect |
| 18. C23×Q8×C53 | C22 | semidirect |
| 20. C53×#393 | C22 | semidirect |
| 21. C2×#95×C53 | C22 | semidirect |
| 24. C24×D53 | Q8 | semidirect |
| 29. C22×Dic106 | C23 | semidirect |
| 37. #13133124 | C23 | semidirect |
| 38. #13133124 | C23 | semidirect |
| 41. C22×Q8×C53 | C23 | semidirect |
| 46. #95×C53 | C23 | semidirect |
| 60. C23×D53 | C2×Q8 | semidirect |
| 136. C2×#393 | D53 | semidirect |
| 139. C2×C53 | #2840 | semidirect |
| 146. C23×Q8 | C2×D53 | semidirect |
| 154. #393 | C2×D53 | semidirect |
| 158. C2×#95 | C2×D53 | semidirect |
| 159. C53 | C2×#2840 | semidirect |
| 170. C22×Q8 | C22×D53 | semidirect |
| 184. #95 | C22×D53 | semidirect |
| 271. C2 | #20282967 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282967 | 2 |
| C2×#16810536 | 2 |
| C2×#16810535 | 2 |
| C2×#16810534 | 2 |
| C2×#16810478 | 2 |
| C2×C53×#393 | 2 |
| C2×#2840 | 53 |