Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 1. #20276504 | C2 | semidirect |
| 2. C2×#16810433 | C2 | semidirect |
| 3. #20276427 | C2 | semidirect |
| 4. C2×#16810405 | C2 | semidirect |
| 5. #20274748 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 35. #13133157 | D4 | semidirect |
| 236. C53 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276504 | 2 |
| C2×#16810433 | 2 |
| #20276427 | 2 |
| C2×#16810405 | 2 |
| #20274748 | 2 |
| #20272820 | 2 |
| C53×#3054 | 2 |
| #13386 | 53 |