Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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×Dic6 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 7. #4855 | C2 | semidirect |
| 8. #4791 | C2 | semidirect |
| 10. #4680 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 63. C3×SD16 | Q8 | semidirect |
| 116. C3×Q8 | C2×Q8 | semidirect |
| 135. Dic6 | SD16 | direct (N × H) |
| 137. C3×C8 | C2×Q8 | semidirect |
| 149. SD16 | Dic6 | direct (N × H) |
| 193. Q8 | C2×Dic6 | semidirect |
| 210. C8 | C2×Dic6 | semidirect |
| 230. C3 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic6 | 2 |
| D4×Dic6 | 2 |
| C3×C4×SD16 | 2 |
| Dic3×SD16 | 2 |
| #5020 | 2 |
| #5008 | 2 |
| #4855 | 2 |
| #4791 | 2 |
| #4761 | 2 |
| #4680 | 2 |
| C8×Dic6 | 2 |
| Q8×SD16 | 3 |