Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20268511 | C2 | semidirect |
| 2. #20268498 | C2 | semidirect |
| 3. #20268144 | C2 | semidirect |
| 4. #20268142 | C2 | semidirect |
| 5. #20268097 | C2 | semidirect |
| 6. #20268081 | C2 | semidirect |
| 8. #20267996 | C2 | semidirect |
| 9. C8×Dic206 | C2 | semidirect |
| 10. #20267882 | C2 | semidirect |
| 121. C103 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268511 | 2 |
| #20268498 | 2 |
| #20268144 | 2 |
| #20268142 | 2 |
| #20268097 | 2 |
| #20268081 | 2 |
| #20268004 | 2 |
| #20267996 | 2 |
| C8×Dic206 | 2 |
| #20267882 | 2 |
| C4×D8×C103 | 2 |
| #3360 | 103 |