Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#16810445 | C2 | semidirect |
| 4. #20275451 | C2 | semidirect |
| 5. #20272824 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 18. #16810427 | C4 | semidirect |
| 19. #16810424 | C4 | semidirect |
| 73. Q16×C53 | C4⋊C4 | semidirect |
| 77. D8×C53 | C4⋊C4 | semidirect |
| 180. C53 | #12955 | semidirect |
| 229. Q16 | #11719919 | semidirect |
| 233. D8 | #11719919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810745 | 2 |
| C2×#16810445 | 2 |
| #20276427 | 2 |
| #20275451 | 2 |
| #20272824 | 2 |
| #20272794 | 2 |
| C2×C53×#360 | 2 |
| #12955 | 53 |