Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C3×#107 | C2 | semidirect |
| 4. #4975 | C2 | semidirect |
| 6. C2×#807 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 23. C2×#107 | D3 | semidirect |
| 194. C3 | #2093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#107 | 2 |
| C2×#821 | 2 |
| #4988 | 2 |
| #4975 | 2 |
| C2×#809 | 2 |
| C2×#807 | 2 |
| #4550 | 2 |
| #2093 | 3 |