Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 1. D4×Dic206 | C2 | semidirect |
| 3. #20268142 | C2 | semidirect |
| 4. #20268122 | C2 | semidirect |
| 5. #20268077 | C2 | semidirect |
| 6. #20268020 | C2 | semidirect |
| 7. #20267997 | C2 | semidirect |
| 8. #20267932 | C2 | semidirect |
| 9. C4×#13110094 | C2 | semidirect |
| 10. C2×#15692946 | C2 | semidirect |
| 11. C8×D4×C103 | C2 | semidirect |
| 79. D4×C103 | SD16 | semidirect |
| 102. Dic206 | #41 | semidirect |
| 129. C103 | #3298 | semidirect |
| 139. C8×D4 | D103 | semidirect |
| 217. D4 | #13110094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic206 | 2 |
| #20268445 | 2 |
| #20268142 | 2 |
| #20268122 | 2 |
| #20268077 | 2 |
| #20268020 | 2 |
| #20267997 | 2 |
| #20267932 | 2 |
| C4×#13110094 | 2 |
| C2×#15692946 | 2 |
| C8×D4×C103 | 2 |
| #3298 | 103 |