Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
| 4. C2×#818 | C2 | semidirect |
| 5. #4554 | C2 | semidirect |
| 13. #901 | C4 | semidirect |
| 22. C2×#108 | D3 | semidirect |
| 168. C3 | #1816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#901 | 2 |
| C2×C3×#108 | 2 |
| #5133 | 2 |
| C2×#818 | 2 |
| #4554 | 2 |
| #1816 | 3 |