Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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×#106 | C2 | semidirect |
| 3. C2×#815 | C2 | semidirect |
| 4. #4988 | C2 | semidirect |
| 5. C2×#809 | C2 | semidirect |
| 15. C2×D24 | C4 | semidirect |
| 20. C2×#106 | D3 | semidirect |
| 78. C3×C8 | C22⋊C4 | semidirect |
| 138. C8 | (C2×D3)⋊C4 | semidirect |
| 159. C3 | #1972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C2×C3×#106 | 2 |
| C2×#815 | 2 |
| #4988 | 2 |
| C2×#809 | 2 |
| #1972 | 3 |