Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 105 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×#125 | C4 | semidirect |
| 34. C4×Dic3 | Q8 | semidirect |
| 38. C4⋊Q8 | Dic3 | semidirect |
| 39. #125 | Dic3 | semidirect |
| 113. C3 | #1994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| C42×Dic3 | 2 |
| #4924 | 2 |
| #4532 | 2 |
| #1994 | 3 |