Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15693069 | C2 | semidirect |
| 2. C2×#15693052 | C2 | semidirect |
| 3. C2×#15693043 | C2 | semidirect |
| 4. #20268372 | C2 | semidirect |
| 5. #20267956 | C2 | semidirect |
| 6. #20267948 | C2 | semidirect |
| 7. #20267939 | C2 | semidirect |
| 8. #20267931 | C2 | semidirect |
| 9. #20267790 | C2 | semidirect |
| 10. #20267757 | C2 | semidirect |
| 11. C2×#103×C103 | C2 | semidirect |
| 54. #13110105 | D4 | semidirect |
| 88. C2×Q8×C103 | D4 | semidirect |
| 170. C103 | #3013 | semidirect |
| 180. C2×#103 | D103 | semidirect |
| 234. C2×Q8 | D412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693069 | 2 |
| C2×#15693052 | 2 |
| C2×#15693043 | 2 |
| #20268372 | 2 |
| #20267956 | 2 |
| #20267948 | 2 |
| #20267939 | 2 |
| #20267931 | 2 |
| #20267790 | 2 |
| #20267757 | 2 |
| C2×#103×C103 | 2 |
| #3013 | 103 |