Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
| 3. #20290245 | C2 | semidirect |
| 5. #20289579 | C2 | semidirect |
| 6. #20289565 | C2 | semidirect |
| 26. #16811033 | C4 | semidirect |
| 27. #16810985 | C4 | semidirect |
| 28. #16810983 | C4 | semidirect |
| 34. C53×#501 | C4 | semidirect |
| 222. #501 | #6157 | semidirect |
| 246. C53 | #9377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291655 | 2 |
| #20290881 | 2 |
| #20290245 | 2 |
| #20290118 | 2 |
| #20289579 | 2 |
| #20289565 | 2 |
| #20285946 | 2 |
| #9377 | 53 |