Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 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. C2×#16810450 | C2 | semidirect |
| 2. C2×#16810430 | C2 | semidirect |
| 3. #20276427 | C2 | semidirect |
| 4. C2×#16810407 | C2 | semidirect |
| 5. #20274779 | C2 | semidirect |
| 6. #20272823 | C2 | semidirect |
| 34. C2×#11719908 | D4 | semidirect |
| 210. C53 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810450 | 2 |
| C2×#16810430 | 2 |
| #20276427 | 2 |
| C2×#16810407 | 2 |
| #20274779 | 2 |
| #20272823 | 2 |
| C53×#3061 | 2 |
| #13385 | 53 |