Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#815 | C2 | semidirect |
| 4. C3×#336 | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 15. (C2×D3)⋊C8 | C4 | semidirect |
| 21. #336 | D3 | semidirect |
| 36. C2×C3×C8 | C2×C4 | semidirect |
| 42. C2×C3⋊C8 | C2×C4 | semidirect |
| 94. C2×C8 | C4×D3 | semidirect |
| 107. C2×D3 | #97 | semidirect |
| 158. C3 | #1749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D3 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#815 | 2 |
| C3×#336 | 2 |
| #4524 | 2 |
| #1749 | 3 |