Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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. C3×C4×C4⋊C4 | C2 | semidirect |
| 3. C2×#809 | C2 | semidirect |
| 4. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 14. #874 | C4 | semidirect |
| 21. C4×C4⋊C4 | D3 | semidirect |
| 37. C3×C4⋊C4 | D4 | semidirect |
| 96. C4⋊C4 | D12 | semidirect |
| 112. C3×C4 | #102 | semidirect |
| 158. C4 | #809 | semidirect |
| 162. C3 | #1982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| C3×C4×C4⋊C4 | 2 |
| C2×#809 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #1982 | 3 |