Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. C3×#330 | C2 | semidirect |
| 4. #4543 | C2 | semidirect |
| 5. #4465 | C2 | semidirect |
| 22. #330 | D3 | direct (N × H) |
| 101. D3 | #330 | direct (N × H) |
| 111. C3 | C2×#330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#125 | 2 |
| D3×#97 | 2 |
| C3×#330 | 2 |
| #4543 | 2 |
| #4465 | 2 |
| C2×#330 | 3 |