Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic206 | C2 | semidirect |
| 3. #20268138 | C2 | semidirect |
| 4. #20268136 | C2 | semidirect |
| 5. #20268081 | C2 | semidirect |
| 6. #20268080 | C2 | semidirect |
| 7. #20267991 | C2 | semidirect |
| 8. #20267989 | C2 | semidirect |
| 9. C8×Dic206 | C2 | semidirect |
| 10. #20267876 | C2 | semidirect |
| 11. C4×SD16×C103 | C2 | semidirect |
| 77. Q8×C103 | #41 | semidirect |
| 99. Dic206 | SD16 | semidirect |
| 126. C103 | #3362 | semidirect |
| 137. C4×SD16 | D103 | semidirect |
| 206. Q8 | #13110105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic206 | 2 |
| #20268462 | 2 |
| #20268138 | 2 |
| #20268136 | 2 |
| #20268081 | 2 |
| #20268080 | 2 |
| #20267991 | 2 |
| #20267989 | 2 |
| C8×Dic206 | 2 |
| #20267876 | 2 |
| C4×SD16×C103 | 2 |
| #3362 | 103 |