Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20285454 | C2 | semidirect |
| 2. #20283620 | C2 | semidirect |
| 3. #20276931 | C2 | semidirect |
| 4. #20276883 | C2 | semidirect |
| 5. #20276792 | C2 | semidirect |
| 6. #20276791 | C2 | semidirect |
| 7. #20276662 | C2 | semidirect |
| 8. #20276612 | C2 | semidirect |
| 9. #20276610 | C2 | semidirect |
| 10. #20276526 | C2 | semidirect |
| 11. C53×#2230 | C2 | semidirect |
| 17. #16811000 | C22 | semidirect |
| 27. #16810734 | C22 | semidirect |
| 31. #16810445 | C22 | semidirect |
| 32. #16810444 | C22 | semidirect |
| 33. #16810437 | C22 | semidirect |
| 34. #16810435 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 38. C53×#498 | C22 | semidirect |
| 40. C53×#365 | C22 | semidirect |
| 41. C53×#364 | C22 | semidirect |
| 113. Q16×C53 | #41 | semidirect |
| 115. D8×C53 | #41 | semidirect |
| 137. Dic212 | #41 | semidirect |
| 142. D424 | #41 | semidirect |
| 219. #2230 | D53 | semidirect |
| 237. #498 | C2×D53 | semidirect |
| 254. #365 | C2×D53 | semidirect |
| 256. #364 | C2×D53 | semidirect |
| 263. C53 | #33688 | semidirect |
| 336. Q16 | #11719949 | semidirect |
| 347. D8 | #11719949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285454 | 2 |
| #20283620 | 2 |
| #20276931 | 2 |
| #20276883 | 2 |
| #20276792 | 2 |
| #20276791 | 2 |
| #20276662 | 2 |
| #20276612 | 2 |
| #20276610 | 2 |
| #20276526 | 2 |
| C53×#2230 | 2 |
| #33688 | 53 |