Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16810437 | C2 | semidirect |
| 3. C2×#16810431 | C2 | semidirect |
| 4. #20276428 | C2 | semidirect |
| 5. C2×#16810425 | C2 | semidirect |
| 6. #20275500 | C2 | semidirect |
| 7. C53×#1379 | C2 | semidirect |
| 54. #13133153 | D4 | semidirect |
| 189. #1379 | D53 | semidirect |
| 216. C53 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285201 | 2 |
| C2×#16810437 | 2 |
| C2×#16810431 | 2 |
| #20276428 | 2 |
| C2×#16810425 | 2 |
| #20275500 | 2 |
| C53×#1379 | 2 |
| #13411 | 53 |