Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 20. #815 | C4 | semidirect |
| 85. C3×C8 | C4⋊C4 | semidirect |
| 86. C3⋊C8 | C4⋊C4 | semidirect |
| 143. C8 | Dic3⋊C4 | semidirect |
| 163. C3 | #1847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#107 | 2 |
| C2×#817 | 2 |
| C2×#815 | 2 |
| #4977 | 2 |
| #4975 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| #1847 | 3 |