Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
292 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
| 4. C2×#819 | C2 | semidirect |
| 5. #4558 | C2 | semidirect |
| 20. C2×#108 | D3 | semidirect |
| 108. C2×D3 | #108 | semidirect |
| 155. C3 | #1810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×C3×#108 | 2 |
| #5126 | 2 |
| C2×#819 | 2 |
| #4558 | 2 |
| #1810 | 3 |