Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 81 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. C3×C4⋊Q8 | C4 | semidirect |
| 7. C3×C4⋊Q8 | C4 | semidirect |
| 12. C3×C4×Q8 | C4 | semidirect |
| 45. C4⋊Q8 | Dic3 | semidirect |
| 46. C4⋊Q8 | Dic3 | semidirect |
| 51. C4×Q8 | Dic3 | semidirect |
| 146. C3 | #1506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| #4932 | 2 |
| #4926 | 2 |
| #4538 | 2 |
| #1506 | 3 |