Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×C3×#125 | C2 | semidirect |
| 3. #5067 | C2 | direct (N × H) |
| 4. C2×#809 | C2 | semidirect |
| 5. C2×#803 | C2 | semidirect |
| 10. C3×#125 | C22 | semidirect |
| 17. #809 | C22 | semidirect |
| 18. #803 | C22 | semidirect |
| 20. C2×#125 | D3 | semidirect |
| 46. #125 | C2×D3 | semidirect |
| 108. C2×C3 | #490 | semidirect |
| 122. C3 | C2×#490 | semidirect |
| 124. C2 | #5067 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#125 | 2 |
| C2×#874 | 2 |
| #5067 | 2 |
| C2×#809 | 2 |
| C2×#803 | 2 |
| C2×#490 | 3 |