Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
908 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
|---|---|---|
| 3. C22×C4⋊Dic3 | C2 | semidirect |
| 4. C22×Dic3⋊C4 | C2 | semidirect |
| 5. C2×C3⋊#95 | C2 | semidirect |
| 6. #4949 | C2 | direct (N × H) |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 20. C2×Dic3⋊C4 | C22 | semidirect |
| 21. C3⋊#95 | C22 | semidirect |
| 173. C2×C3 | #399 | semidirect |
| 199. C3 | C2×#399 | semidirect |
| 201. C2 | #4949 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×Dic3⋊C4 | 2 |
| C2×C3⋊#95 | 2 |
| #4949 | 2 |
| C2×#399 | 3 |