Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
198 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C3×#493 | C2 | semidirect |
| 2. C2×#827 | C2 | semidirect |
| 3. C2×#826 | C2 | semidirect |
| 4. #4696 | C2 | semidirect |
| 5. #4461 | C2 | semidirect |
| 21. #493 | D3 | semidirect |
| 37. C3⋊C16 | D4 | semidirect |
| 114. C3 | #2250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#493 | 2 |
| C2×#827 | 2 |
| C2×#826 | 2 |
| #4696 | 2 |
| #4461 | 2 |
| #2250 | 3 |