Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×#818 | C2 | semidirect |
| 3. C2×#812 | C2 | semidirect |
| 4. #4564 | C2 | semidirect |
| 5. #4562 | C2 | semidirect |
| 9. C3×#135 | C4 | semidirect |
| 33. C3×Q16 | C2×C4 | semidirect |
| 36. C3×D8 | C2×C4 | semidirect |
| 46. #135 | Dic3 | semidirect |
| 83. Q16 | C2×Dic3 | semidirect |
| 86. D8 | C2×Dic3 | semidirect |
| 141. C3 | #2139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#135 | 2 |
| C2×#818 | 2 |
| C2×#812 | 2 |
| #4564 | 2 |
| #4562 | 2 |
| #2139 | 3 |