Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×C8 | C2 | semidirect |
| 3. C2×#821 | C2 | semidirect |
| 4. #4935 | C2 | semidirect |
| 13. #874 | C4 | semidirect |
| 18. C2×C4×C8 | D3 | semidirect |
| 33. C2×C3×C8 | D4 | semidirect |
| 80. C2×C8 | D12 | semidirect |
| 95. C3×C4 | #102 | semidirect |
| 135. C4 | #821 | semidirect |
| 138. C3 | #1957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#821 | 2 |
| #4935 | 2 |
| #1957 | 3 |