Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C3×C4⋊C16 | C2 | semidirect |
| 4. Dic3⋊C16 | C2 | semidirect |
| 5. C4⋊(C3⋊C16) | C2 | semidirect |
| 21. C4⋊C16 | D3 | semidirect |
| 85. C3×C4 | M32 | semidirect |
| 90. Dic3 | M32 | semidirect |
| 119. C4 | #798 | semidirect |
| 122. C3 | #2150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#798 | 2 |
| C4×D3×C8 | 2 |
| C3×C4⋊C16 | 2 |
| Dic3⋊C16 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2150 | 3 |