Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 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 |
|---|---|---|
| 2. #20277528 | C2 | semidirect |
| 3. #20273312 | C2 | semidirect |
| 4. #20273262 | C2 | semidirect |
| 5. #20272580 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#1980 | C2 | semidirect |
| 9. #16811010 | C4 | semidirect |
| 10. #16810985 | C4 | semidirect |
| 54. #13133128 | C2×C4 | semidirect |
| 63. C4⋊Q8×C53 | C2×C4 | semidirect |
| 64. #127×C53 | C2×C4 | semidirect |
| 217. #1980 | D53 | semidirect |
| 252. C53 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D53 | semidirect |
| 261. #127 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285698 | 2 |
| #20277528 | 2 |
| #20273312 | 2 |
| #20273262 | 2 |
| #20272580 | 2 |
| #20272571 | 2 |
| C53×#1980 | 2 |
| #9381 | 53 |