Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
196 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 196 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 |
|---|---|---|
| 3. C3×C4×C16 | C2 | semidirect |
| 4. #4502 | C2 | semidirect |
| 5. C4×C3⋊C16 | C2 | semidirect |
| 16. #798 | C4 | direct (N × H) |
| 21. C4×C16 | D3 | semidirect |
| 33. C3×C16 | C2×C4 | semidirect |
| 34. C3⋊C16 | C2×C4 | semidirect |
| 69. C16 | C4×D3 | semidirect |
| 73. C3×C4 | M32 | semidirect |
| 98. C4 | #798 | direct (N × H) |
| 101. C3 | C4×M32 | 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 |
| #4502 | 2 |
| C4×C3⋊C16 | 2 |
| C4×M32 | 3 |