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. #20276503 | C2 | semidirect |
| 3. #20276427 | C2 | semidirect |
| 4. C2×#16810404 | C2 | semidirect |
| 5. #20274745 | C2 | semidirect |
| 6. #20272822 | C2 | semidirect |
| 7. C2×C53×#360 | C2 | semidirect |
| 72. M32×C53 | D4 | semidirect |
| 203. C2×#360 | 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 |
|---|---|
| #20284320 | 2 |
| #20276503 | 2 |
| #20276427 | 2 |
| C2×#16810404 | 2 |
| #20274745 | 2 |
| #20272822 | 2 |
| C2×C53×#360 | 2 |
| #13386 | 53 |