Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×#204 | C2 | semidirect |
| 3. C2×#821 | C2 | semidirect |
| 4. #4929 | C2 | semidirect |
| 5. C3×#336 | C2 | semidirect |
| 23. #336 | D3 | semidirect |
| 41. C2×Dic6 | D4 | semidirect |
| 44. C2×C3×C8 | D4 | semidirect |
| 68. C2×C3×C4 | SD16 | semidirect |
| 107. C2×C8 | D12 | semidirect |
| 145. C2×C4 | #204 | semidirect |
| 172. C3 | #2014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×#874 | 2 |
| C2×#821 | 2 |
| #4929 | 2 |
| C3×#336 | 2 |
| #2014 | 3 |