Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#102 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. C2×#815 | C2 | semidirect |
| 6. #4977 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 15. #940 | C4 | semidirect |
| 29. C2×#102 | D3 | semidirect |
| 55. C2×C3×C8 | D4 | semidirect |
| 64. C2×C3⋊C8 | D4 | semidirect |
| 142. C2×C8 | #67 | semidirect |
| 235. C3 | #1961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#821 | 2 |
| C2×#815 | 2 |
| #4977 | 2 |
| C2×#809 | 2 |
| #1961 | 3 |