Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20268231 | C2 | semidirect |
| 2. C2×#15692965 | C2 | semidirect |
| 3. #20268066 | C2 | semidirect |
| 4. #20267604 | C2 | semidirect |
| 5. #20267598 | C2 | semidirect |
| 6. #20267575 | C2 | semidirect |
| 9. C2×Dic412 | C22 | semidirect |
| 13. #15692961 | C22 | semidirect |
| 14. C2×C103⋊C16 | C22 | semidirect |
| 15. #15692957 | C22 | semidirect |
| 92. C103 | #2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268231 | 2 |
| C2×#15692965 | 2 |
| #20268066 | 2 |
| #20267604 | 2 |
| #20267598 | 2 |
| #20267575 | 2 |
| #576×C103 | 2 |
| #2194 | 103 |