Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 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. #20276503 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. C2×#16810425 | C2 | semidirect |
| 5. #20274779 | C2 | semidirect |
| 6. #20272811 | C2 | semidirect |
| 7. C2×C53×#350 | C2 | semidirect |
| 63. M32×C53 | D4 | semidirect |
| 181. C2×#350 | D53 | semidirect |
| 210. C53 | #13387 | semidirect |
| 236. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284363 | 2 |
| #20276503 | 2 |
| C2×#16810437 | 2 |
| C2×#16810425 | 2 |
| #20274779 | 2 |
| #20272811 | 2 |
| C2×C53×#350 | 2 |
| #13387 | 53 |