Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 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×C3×#102 | C2 | semidirect |
| 3. #5221 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. C2×C8×Dic3 | C2 | semidirect |
| 6. #4988 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 16. C2×#213 | C4 | semidirect |
| 28. C2×#102 | D3 | semidirect |
| 108. C2×Dic3 | D8 | semidirect |
| 114. C3⋊C8 | C22⋊C4 | semidirect |
| 233. C3 | #1970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#213 | 2 |
| C2×C3×#102 | 2 |
| #5221 | 2 |
| C2×#821 | 2 |
| C2×C8×Dic3 | 2 |
| #4988 | 2 |
| C2×#807 | 2 |
| #1970 | 3 |