Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 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×C3×#125 | C2 | semidirect |
| 3. #5066 | C2 | direct (N × H) |
| 6. C2×#808 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 8. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 13. C3×#125 | C22 | semidirect |
| 27. #808 | C22 | semidirect |
| 28. #807 | C22 | semidirect |
| 29. C4⋊(C3⋊C8) | C22 | semidirect |
| 30. C2×#125 | D3 | semidirect |
| 71. #125 | C2×D3 | semidirect |
| 180. C2×C3 | #478 | semidirect |
| 201. C3 | C2×#478 | semidirect |
| 203. C2 | #5066 | 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×C4×D12 | 2 |
| #5066 | 2 |
| C2×#809 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#478 | 3 |