Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×C22⋊C8 | C2 | semidirect |
| 3. #5212 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 12. C2×#235 | C4 | semidirect |
| 26. C2×C22⋊C8 | D3 | semidirect |
| 103. D12 | C22⋊C4 | semidirect |
| 107. Dic6 | C22⋊C4 | semidirect |
| 223. C3 | #1788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C2×C3×C22⋊C8 | 2 |
| #5212 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #1788 | 3 |