Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 432 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×#16810434 | C2 | semidirect |
| 4. #20276428 | C2 | semidirect |
| 5. #20274748 | C2 | semidirect |
| 6. #20272821 | C2 | semidirect |
| 7. C2×C53×#349 | C2 | semidirect |
| 73. M32×C53 | D4 | semidirect |
| 205. C2×#349 | D53 | semidirect |
| 236. C53 | #13386 | semidirect |
| 269. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284324 | 2 |
| #20276503 | 2 |
| C2×#16810434 | 2 |
| #20276428 | 2 |
| #20274748 | 2 |
| #20272821 | 2 |
| C2×C53×#349 | 2 |
| #13386 | 53 |