Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 7. C2×C3×C42 | C4 | semidirect |
| 12. C3⋊#95 | C4 | semidirect |
| 14. #830 | C4 | semidirect |
| 37. C2×C42 | Dic3 | semidirect |
| 144. C3 | #1284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C22⋊C4 | 2 |
| #5211 | 2 |
| #5207 | 2 |
| #1284 | 3 |