Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16810435 | C2 | semidirect |
| 3. #20276427 | C2 | semidirect |
| 4. C2×#16810425 | C2 | semidirect |
| 5. #20275501 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C2×C53×#359 | C2 | semidirect |
| 69. #108×C53 | D4 | semidirect |
| 185. C2×#359 | D53 | semidirect |
| 216. C53 | #13411 | semidirect |
| 253. #108 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285202 | 2 |
| C2×#16810435 | 2 |
| #20276427 | 2 |
| C2×#16810425 | 2 |
| #20275501 | 2 |
| #20272803 | 2 |
| C2×C53×#359 | 2 |
| #13411 | 53 |