Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C2×#944 | C2 | semidirect |
| 5. C2×C3×#103 | C2 | semidirect |
| 6. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4818 | C2 | direct (N × H) |
| 17. #944 | C22 | semidirect |
| 29. C3×#103 | C22 | semidirect |
| 30. Dic3⋊C8 | C22 | semidirect |
| 31. #810 | C22 | semidirect |
| 39. C2×#103 | D3 | semidirect |
| 95. #103 | C2×D3 | semidirect |
| 115. C2×Dic3 | SD16 | semidirect |
| 176. Dic3 | C2×SD16 | semidirect |
| 208. C2×C3 | #461 | semidirect |
| 229. C3 | C2×#461 | semidirect |
| 231. C2 | #4818 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#944 | 2 |
| C22×#215 | 2 |
| C22×#204 | 2 |
| C2×#893 | 2 |
| C2×C3×#103 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#810 | 2 |
| #4818 | 2 |
| C2×#461 | 3 |