Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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×#389 | C2 | semidirect |
| 3. C2×#809 | C2 | semidirect |
| 4. C2×#809 | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 22. #389 | D3 | semidirect |
| 45. C3×C4⋊C4 | D4 | semidirect |
| 117. C4⋊C4 | D12 | semidirect |
| 198. C3 | #2041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| C3×#389 | 2 |
| C2×#809 | 2 |
| #4524 | 2 |
| #2041 | 3 |