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. C2×#16811513 | C2 | semidirect |
| 4. #20290524 | C2 | semidirect |
| 5. #20289795 | C2 | semidirect |
| 6. #20289783 | C2 | semidirect |
| 10. #16811664 | C4 | semidirect |
| 11. #16811663 | C4 | semidirect |
| 18. #16811540 | C4 | semidirect |
| 19. #16811539 | C4 | semidirect |
| 25. #16810431 | C4 | semidirect |
| 26. #16810430 | C4 | semidirect |
| 27. #16810429 | C4 | semidirect |
| 28. C53×#359 | C4 | semidirect |
| 39. #13133292 | C2×C4 | semidirect |
| 44. #13133285 | C2×C4 | semidirect |
| 64. C2×#11719908 | C2×C4 | semidirect |
| 65. #13133153 | C2×C4 | semidirect |
| 68. C2×C16×C53 | C2×C4 | semidirect |
| 69. #108×C53 | C2×C4 | semidirect |
| 203. #359 | #6157 | semidirect |
| 206. C53 | #12649 | semidirect |
| 234. C2×C16 | C2×#6157 | semidirect |
| 237. #108 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291469 | 2 |
| #20291035 | 2 |
| C2×#16811513 | 2 |
| #20290524 | 2 |
| #20289795 | 2 |
| #20289783 | 2 |
| #20276441 | 2 |
| #12649 | 53 |