Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
240 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 61 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. #5080 | C2 | semidirect |
| 3. #5019 | C2 | semidirect |
| 4. #5007 | C2 | semidirect |
| 5. #4547 | C2 | semidirect |
| 6. D4⋊(C3⋊C8) | C2 | semidirect |
| 7. D4⋊(C3⋊C8) | C2 | semidirect |
| 83. C3×D4 | SD16 | semidirect |
| 152. D4 | #214 | semidirect |
| 189. C3 | #1654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#547 | 2 |
| #5080 | 2 |
| #5019 | 2 |
| #5007 | 2 |
| #4547 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #1654 | 3 |