Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20268322 | C2 | semidirect |
| 2. #20268192 | C2 | semidirect |
| 3. #20268174 | C2 | semidirect |
| 4. #20268144 | C2 | semidirect |
| 5. #20268032 | C2 | semidirect |
| 6. #20268018 | C2 | semidirect |
| 7. #20267885 | C2 | semidirect |
| 8. #20267882 | C2 | semidirect |
| 9. D8×Dic103 | C2 | semidirect |
| 10. C2×C8×Dic103 | C2 | semidirect |
| 119. C103 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268322 | 2 |
| #20268192 | 2 |
| #20268174 | 2 |
| #20268144 | 2 |
| #20268032 | 2 |
| #20268018 | 2 |
| #20267885 | 2 |
| #20267882 | 2 |
| D8×Dic103 | 2 |
| C2×C8×Dic103 | 2 |
| #466×C103 | 2 |
| #3168 | 103 |