Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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×C3×#108 | C2 | semidirect |
| 3. C2×#812 | C2 | semidirect |
| 4. #4495 | C2 | direct (N × H) |
| 16. C3×#108 | C22 | semidirect |
| 18. #812 | C22 | semidirect |
| 22. C2×#108 | D3 | semidirect |
| 59. #108 | C2×D3 | semidirect |
| 136. C2×C3 | #361 | semidirect |
| 151. C3 | C2×#361 | semidirect |
| 155. C2 | #4495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C2×C3×#108 | 2 |
| C2×#812 | 2 |
| #4495 | 2 |
| C2×#361 | 3 |