Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 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. D4×Dic6 | C2 | semidirect |
| 4. #5007 | C2 | semidirect |
| 5. #4874 | C2 | semidirect |
| 6. #4759 | C2 | semidirect |
| 7. #4682 | C2 | semidirect |
| 8. C8×Dic6 | C2 | semidirect |
| 44. C3×D8 | Q8 | semidirect |
| 79. C3×D4 | C2×Q8 | semidirect |
| 91. Dic6 | D8 | direct (N × H) |
| 93. C3×C8 | C2×Q8 | semidirect |
| 102. D8 | Dic6 | direct (N × H) |
| 133. D4 | C2×Dic6 | semidirect |
| 145. C8 | C2×Dic6 | semidirect |
| 162. C3 | Q8×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic6 | 2 |
| C3×C4×D8 | 2 |
| Dic3×D8 | 2 |
| #5007 | 2 |
| #4874 | 2 |
| #4759 | 2 |
| #4682 | 2 |
| C8×Dic6 | 2 |
| Q8×D8 | 3 |