Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 6. #4701 | C2 | semidirect |
| 32. C2×C3×C8 | Q8 | semidirect |
| 78. C2×C8 | Dic6 | semidirect |
| 123. C3 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C2×C3×#97 | 2 |
| #5102 | 2 |
| #5101 | 2 |
| #4924 | 2 |
| #4701 | 2 |
| #2961 | 3 |