Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
848 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 848 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×#102 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 6. #4987 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 17. C2×D3×D4 | C4 | semidirect |
| 20. C22×C3×C8 | C22 | semidirect |
| 21. C2×C3×C4⋊C4 | C22 | semidirect |
| 23. C2×C4⋊Dic3 | C22 | semidirect |
| 24. C22×C3⋊C8 | C22 | semidirect |
| 35. C2×#102 | D3 | semidirect |
| 100. C22×C8 | C2×D3 | semidirect |
| 102. C2×C4⋊C4 | C2×D3 | semidirect |
| 142. C3×D4 | C22⋊C4 | semidirect |
| 162. D12 | C22⋊C4 | semidirect |
| 247. C2×D3 | #102 | semidirect |
| 292. D4 | (C2×D3)⋊C4 | semidirect |
| 360. C3 | #1786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D4 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#821 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| #4987 | 2 |
| C2×#809 | 2 |
| #1786 | 3 |