Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
262 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 2. C2×C3×#108 | C2 | semidirect |
| 3. C2×#824 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 27. C2×#108 | D3 | semidirect |
| 212. C3 | #2052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| C2×C3×#108 | 2 |
| C2×#824 | 2 |
| #5133 | 2 |
| #5110 | 2 |
| C2×#816 | 2 |
| #4554 | 2 |
| #2052 | 3 |