Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 13. C3×#106 | C4 | semidirect |
| 46. #106 | Dic3 | semidirect |
| 65. C3×C8 | C4⋊C4 | semidirect |
| 113. C8 | C4⋊Dic3 | semidirect |
| 131. C3 | #1941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#106 | 2 |
| C2×#817 | 2 |
| C2×C8×Dic3 | 2 |
| #4984 | 2 |
| #4529 | 2 |
| #1941 | 3 |