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. #20285451 | C2 | semidirect |
| 2. #20283620 | C2 | semidirect |
| 3. #20276928 | C2 | semidirect |
| 4. #20276887 | C2 | semidirect |
| 5. #20276886 | C2 | semidirect |
| 6. #20276788 | C2 | semidirect |
| 7. #20276659 | C2 | semidirect |
| 8. #20276616 | C2 | semidirect |
| 9. #20276614 | C2 | semidirect |
| 10. #20276526 | C2 | semidirect |
| 11. C53×#2213 | C2 | semidirect |
| 16. #16811021 | C22 | semidirect |
| 26. #16810735 | C22 | semidirect |
| 30. #16810447 | C22 | semidirect |
| 31. #16810446 | C22 | semidirect |
| 32. #16810444 | C22 | semidirect |
| 33. #16810436 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 39. C53×#493 | C22 | semidirect |
| 41. C53×#364 | C22 | semidirect |
| 42. C53×#361 | C22 | semidirect |
| 113. Q16×C53 | #41 | semidirect |
| 119. D8×C53 | #41 | semidirect |
| 141. Dic212 | #41 | semidirect |
| 142. D424 | #41 | semidirect |
| 221. #2213 | D53 | semidirect |
| 238. #493 | C2×D53 | semidirect |
| 256. #364 | C2×D53 | semidirect |
| 258. #361 | C2×D53 | semidirect |
| 263. C53 | #33688 | semidirect |
| 336. Q16 | #11719947 | semidirect |
| 347. D8 | #11719947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285451 | 2 |
| #20283620 | 2 |
| #20276928 | 2 |
| #20276887 | 2 |
| #20276886 | 2 |
| #20276788 | 2 |
| #20276659 | 2 |
| #20276616 | 2 |
| #20276614 | 2 |
| #20276526 | 2 |
| C53×#2213 | 2 |
| #33688 | 53 |