Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 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. #20285091 | C2 | semidirect |
| 3. #20273428 | C2 | semidirect |
| 4. #20273313 | C2 | semidirect |
| 5. #20273227 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#3215 | C2 | semidirect |
| 49. #13133128 | D4 | semidirect |
| 57. C4⋊Q8×C53 | D4 | semidirect |
| 58. C4⋊Q8×C53 | D4 | semidirect |
| 72. C4⋊C8×C53 | D4 | semidirect |
| 195. #3215 | D53 | semidirect |
| 231. C53 | #10096 | semidirect |
| 241. C4⋊Q8 | C22⋊D53 | semidirect |
| 242. C4⋊Q8 | C22⋊D53 | semidirect |
| 265. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285091 | 2 |
| #20280823 | 2 |
| #20273428 | 2 |
| #20273313 | 2 |
| #20273227 | 2 |
| #20272607 | 2 |
| C53×#3215 | 2 |
| #10096 | 53 |