Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 217 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. #5229 | C2 | semidirect |
| 5. #4980 | C2 | semidirect |
| 6. #4980 | C2 | semidirect |
| 7. Dic3×C4⋊C4 | C2 | semidirect |
| 13. C3×C22⋊Q8 | C4 | semidirect |
| 71. C22⋊Q8 | Dic3 | semidirect |
| 224. C3 | #2332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊Q8 | 2 |
| #5229 | 2 |
| #5211 | 2 |
| C4×#217 | 2 |
| #4980 | 2 |
| Dic3×C4⋊C4 | 2 |
| #4951 | 2 |
| #2332 | 3 |