Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
848 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 133 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. C3×#380 | C2 | semidirect |
| 3. C2×#830 | C2 | semidirect |
| 4. C2×#809 | C2 | semidirect |
| 11. C22×D12 | C4 | semidirect |
| 13. C2×C3×C4⋊C4 | C22 | semidirect |
| 15. C22×C3⋊C8 | C22 | semidirect |
| 22. #380 | D3 | semidirect |
| 56. C2×C4⋊C4 | C2×D3 | semidirect |
| 90. D12 | C22⋊C4 | semidirect |
| 121. C22×C3 | #102 | semidirect |
| 185. C22 | #809 | semidirect |
| 195. C3 | #1786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C3×#380 | 2 |
| C2×#830 | 2 |
| C2×#809 | 2 |
| #1786 | 3 |