Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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. #4699 | C2 | semidirect |
| 4. C3×C4⋊C16 | C2 | semidirect |
| 5. #4503 | C2 | semidirect |
| 20. C4⋊C16 | D3 | semidirect |
| 83. C3×C4 | SD32 | semidirect |
| 113. C4 | #800 | semidirect |
| 116. C3 | #2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#800 | 2 |
| #4699 | 2 |
| C4×D24 | 2 |
| C3×C4⋊C16 | 2 |
| #4503 | 2 |
| #2208 | 3 |