Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
192 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 87 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. D4×C3⋊C8 | C2 | semidirect |
| 3. D4⋊(C3⋊C8) | C2 | semidirect |
| 4. #4457 | C2 | semidirect |
| 5. #4455 | C2 | semidirect |
| 24. C3×D8 | C8 | semidirect |
| 46. C3×D4 | C2×C8 | semidirect |
| 54. C3×C8 | C2×C8 | semidirect |
| 60. D8 | C3⋊C8 | semidirect |
| 81. D4 | C2×C3⋊C8 | semidirect |
| 92. C8 | C2×C3⋊C8 | semidirect |
| 106. C3 | #1580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D8 | 2 |
| D4×C3⋊C8 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4457 | 2 |
| #4455 | 2 |
| #1580 | 3 |