Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 4. #5210 | C2 | semidirect |
| 5. #4946 | C2 | semidirect |
| 6. #4942 | C2 | semidirect |
| 16. C2×#217 | C4 | semidirect |
| 21. C2×Dic3⋊C4 | C22 | semidirect |
| 22. C3⋊#95 | C22 | semidirect |
| 42. C22×Dic3 | C2×C4 | semidirect |
| 49. #217 | C2×C4 | semidirect |
| 50. #217 | C2×C4 | semidirect |
| 73. C23×C3 | C4⋊C4 | semidirect |
| 142. C23 | Dic3⋊C4 | semidirect |
| 189. C3 | #2315 | semidirect |
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 |
| #5210 | 2 |
| #4946 | 2 |
| #4942 | 2 |
| #2315 | 3 |