Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16810434 | C2 | semidirect |
| 3. #20276425 | C2 | semidirect |
| 4. C2×#16810404 | C2 | semidirect |
| 5. #20274749 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#2159 | C2 | semidirect |
| 69. M32×C53 | D4 | semidirect |
| 202. #2159 | D53 | semidirect |
| 236. C53 | #13386 | semidirect |
| 269. M32 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284325 | 2 |
| C2×#16810434 | 2 |
| #20276425 | 2 |
| C2×#16810404 | 2 |
| #20274749 | 2 |
| #20272820 | 2 |
| C53×#2159 | 2 |
| #13386 | 53 |