Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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×#97 | C2 | semidirect |
| 4. C2×Dic3⋊C8 | C2 | semidirect |
| 5. C2×#803 | C2 | semidirect |
| 6. #4705 | C2 | direct (N × H) |
| 19. C3×#97 | C22 | semidirect |
| 21. Dic3⋊C8 | C22 | semidirect |
| 22. #803 | C22 | semidirect |
| 28. C2×#97 | D3 | semidirect |
| 67. #97 | C2×D3 | semidirect |
| 155. C2×C3 | #432 | semidirect |
| 175. C3 | C2×#432 | semidirect |
| 177. C2 | #4705 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D3 | 2 |
| C2×C3×#97 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#803 | 2 |
| #4705 | 2 |
| C2×#432 | 3 |