Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 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×C4×C8 | C2 | semidirect |
| 3. C2×#821 | C2 | semidirect |
| 4. C2×#818 | C2 | semidirect |
| 5. #4939 | C2 | semidirect |
| 15. C2×D24 | C4 | semidirect |
| 22. C2×C4×C8 | D3 | semidirect |
| 66. C2×C3×C4 | D8 | semidirect |
| 80. C3×C8 | C22⋊C4 | semidirect |
| 133. C2×C4 | D24 | semidirect |
| 141. C8 | (C2×D3)⋊C4 | semidirect |
| 164. C3 | #1970 | 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×C4×C8 | 2 |
| C2×#821 | 2 |
| C2×#818 | 2 |
| #4939 | 2 |
| #1970 | 3 |