Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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×#824 | C2 | semidirect |
| 6. #5120 | C2 | semidirect |
| 7. #5101 | C2 | semidirect |
| 19. C2×#204 | C4 | semidirect |
| 28. C2×#108 | D3 | semidirect |
| 207. C3 | #1977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×C3×#108 | 2 |
| C2×#824 | 2 |
| #5131 | 2 |
| C2×#823 | 2 |
| #5120 | 2 |
| #5101 | 2 |
| #1977 | 3 |