Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×Dic6 | C2 | semidirect |
| 4. C2×#816 | C2 | semidirect |
| 6. C3×#336 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 22. C2×#204 | C4 | semidirect |
| 33. #336 | D3 | semidirect |
| 101. C2×C3×C4 | SD16 | semidirect |
| 124. Dic6 | C22⋊C4 | semidirect |
| 216. C2×C4 | #204 | semidirect |
| 256. C3 | #1880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×C4×Dic6 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #4939 | 2 |
| C3×#336 | 2 |
| #4551 | 2 |
| #1880 | 3 |