Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. #20290930 | C2 | semidirect |
| 4. #20290523 | C2 | semidirect |
| 5. #20289796 | C2 | semidirect |
| 6. #20289782 | C2 | semidirect |
| 10. #16811664 | C4 | semidirect |
| 11. #16811664 | C4 | semidirect |
| 12. #16811663 | C4 | semidirect |
| 13. #16811663 | C4 | semidirect |
| 21. #16811538 | C4 | semidirect |
| 22. #16811537 | C4 | semidirect |
| 29. #16810434 | C4 | semidirect |
| 30. #16810433 | C4 | semidirect |
| 31. #16810432 | C4 | semidirect |
| 32. C53×#360 | C4 | semidirect |
| 47. D53⋊C16 | C2×C4 | semidirect |
| 49. #13133288 | C2×C4 | semidirect |
| 74. #13133157 | C2×C4 | semidirect |
| 78. #13133149 | C2×C4 | semidirect |
| 80. M32×C53 | C2×C4 | semidirect |
| 81. #106×C53 | C2×C4 | semidirect |
| 231. #360 | #6157 | semidirect |
| 237. C53 | #12649 | semidirect |
| 266. M32 | C2×#6157 | semidirect |
| 276. #106 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291469 | 2 |
| #20291029 | 2 |
| #20290930 | 2 |
| #20290523 | 2 |
| #20289796 | 2 |
| #20289782 | 2 |
| #20276449 | 2 |
| #12649 | 53 |