Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20273266 | C2 | semidirect |
| 5. #20272580 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#1986 | C2 | semidirect |
| 9. #16811015 | C4 | semidirect |
| 10. #16810985 | C4 | semidirect |
| 54. #13133128 | C2×C4 | semidirect |
| 62. C4⋊Q8×C53 | C2×C4 | semidirect |
| 63. C4⋊Q8×C53 | C2×C4 | semidirect |
| 201. #1986 | D53 | semidirect |
| 235. C53 | #9379 | semidirect |
| 242. C4⋊Q8 | C4×D53 | semidirect |
| 243. C4⋊Q8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285714 | 2 |
| #20277528 | 2 |
| #20273312 | 2 |
| #20273266 | 2 |
| #20272580 | 2 |
| #20272571 | 2 |
| C53×#1986 | 2 |
| #9379 | 53 |