Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#100 | C2 | semidirect |
| 3. #5221 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. #5133 | C2 | semidirect |
| 11. #1004 | C4 | semidirect |
| 15. C2×C3×M16 | C22 | semidirect |
| 17. C2×C4⋊Dic3 | C22 | semidirect |
| 18. C2×C4×Dic3 | C22 | semidirect |
| 26. C2×#100 | D3 | semidirect |
| 67. C2×M16 | C2×D3 | semidirect |
| 102. D12 | C22⋊C4 | semidirect |
| 106. Dic6 | C22⋊C4 | semidirect |
| 217. C3 | #1792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1004 | 2 |
| C2×C3×#100 | 2 |
| #5221 | 2 |
| C2×#825 | 2 |
| #5133 | 2 |
| #1792 | 3 |