Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×C3×#103 | C2 | semidirect |
| 3. C2×#835 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 15. C2×D3×Q8 | C4 | semidirect |
| 35. C2×#103 | D3 | semidirect |
| 117. C3×Q8 | C22⋊C4 | semidirect |
| 148. Dic6 | C22⋊C4 | semidirect |
| 210. C2×D3 | #103 | semidirect |
| 236. Q8 | (C2×D3)⋊C4 | semidirect |
| 296. C3 | #1787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C2×C3×#103 | 2 |
| C2×#835 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#816 | 2 |
| #4987 | 2 |
| C2×#810 | 2 |
| #1787 | 3 |