Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 2. #20290881 | C2 | semidirect |
| 4. #20290231 | C2 | semidirect |
| 5. #20289611 | C2 | semidirect |
| 6. #20289584 | C2 | semidirect |
| 24. #16810918 | C4 | semidirect |
| 25. #16810914 | C4 | semidirect |
| 26. #16810910 | C4 | semidirect |
| 32. C53×#477 | C4 | semidirect |
| 146. Q8×C53 | #103 | semidirect |
| 161. D212 | #103 | semidirect |
| 224. #477 | #6157 | semidirect |
| 246. C53 | #9317 | semidirect |
| 360. Q8 | #13133280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291633 | 2 |
| #20290881 | 2 |
| #20290590 | 2 |
| #20290231 | 2 |
| #20289611 | 2 |
| #20289584 | 2 |
| #20284529 | 2 |
| #9317 | 53 |