Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #20268142 | C2 | semidirect |
| 4. #20268127 | C2 | semidirect |
| 5. #20268087 | C2 | semidirect |
| 6. #20268032 | C2 | semidirect |
| 7. #20268002 | C2 | semidirect |
| 8. #20267949 | C2 | semidirect |
| 9. C4×Dic412 | C2 | semidirect |
| 10. C2×#15692946 | C2 | semidirect |
| 77. D4×C103 | Q16 | semidirect |
| 123. C103 | #3299 | semidirect |
| 208. D4 | Dic412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268498 | 2 |
| D4×Dic206 | 2 |
| #20268142 | 2 |
| #20268127 | 2 |
| #20268087 | 2 |
| #20268032 | 2 |
| #20268002 | 2 |
| #20267949 | 2 |
| C4×Dic412 | 2 |
| C2×#15692946 | 2 |
| C8×D4×C103 | 2 |
| #3299 | 103 |