Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #20285714 | C2 | semidirect |
| 3. #20275660 | C2 | semidirect |
| 4. #20273314 | C2 | semidirect |
| 5. #20273158 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#3110 | C2 | semidirect |
| 52. C4⋊#88322 | D4 | semidirect |
| 63. C4⋊Q8×C53 | D4 | semidirect |
| 64. C4⋊Q8×C53 | D4 | semidirect |
| 83. #97×C53 | D4 | semidirect |
| 222. #3110 | D53 | semidirect |
| 260. C53 | #10008 | semidirect |
| 270. C4⋊Q8 | C22⋊D53 | semidirect |
| 271. C4⋊Q8 | C22⋊D53 | semidirect |
| 309. #97 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285714 | 2 |
| #20279654 | 2 |
| #20275660 | 2 |
| #20273314 | 2 |
| #20273158 | 2 |
| #20272570 | 2 |
| C53×#3110 | 2 |
| #10008 | 53 |