Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. C2×#818 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 16. C3×C22⋊C8 | C4 | semidirect |
| 39. C2×C3×C8 | C2×C4 | semidirect |
| 56. C22⋊C8 | Dic3 | semidirect |
| 101. C2×C8 | C2×Dic3 | semidirect |
| 114. C22×C3 | #107 | semidirect |
| 170. C22 | #818 | semidirect |
| 184. C3 | #1852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic3 | 2 |
| C2×C3×C22⋊C8 | 2 |
| #5212 | 2 |
| C2×#818 | 2 |
| #4551 | 2 |
| #1852 | 3 |