Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
580 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 96 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. #20291633 | C2 | semidirect |
| 2. #20290882 | C2 | semidirect |
| 3. #20290590 | C2 | semidirect |
| 4. #20290223 | C2 | semidirect |
| 5. #20289611 | C2 | semidirect |
| 6. #20289584 | C2 | semidirect |
| 25. #16810823 | C4 | semidirect |
| 27. #16810819 | C4 | semidirect |
| 29. #16810815 | C4 | semidirect |
| 32. C53×#460 | C4 | semidirect |
| 162. Q8×C53 | #102 | semidirect |
| 188. D212 | #102 | semidirect |
| 257. #460 | #6157 | semidirect |
| 277. C53 | #9318 | semidirect |
| 404. Q8 | #13133279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291633 | 2 |
| #20290882 | 2 |
| #20290590 | 2 |
| #20290223 | 2 |
| #20289611 | 2 |
| #20289584 | 2 |
| #20284192 | 2 |
| #9318 | 53 |