Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. C3×#366 | C2 | semidirect |
| 5. #4505 | C2 | semidirect |
| 6. #4490 | C2 | semidirect |
| 7. #4489 | C2 | semidirect |
| 20. #798 | C4 | semidirect |
| 27. #366 | D3 | semidirect |
| 41. C3×C16 | C2×C4 | semidirect |
| 42. C3⋊C16 | C2×C4 | semidirect |
| 82. C16 | C4×D3 | semidirect |
| 122. C3 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#798 | 2 |
| #4880 | 2 |
| D3×#107 | 2 |
| C3×#366 | 2 |
| #4505 | 2 |
| #4490 | 2 |
| #4489 | 2 |
| #2159 | 3 |