Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. C3×#533 | C2 | semidirect |
| 3. #5087 | C2 | semidirect |
| 4. #5084 | C2 | semidirect |
| 5. #5066 | C2 | semidirect |
| 7. #4995 | C2 | semidirect |
| 8. #4924 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 13. C3×C4⋊Q8 | C22 | semidirect |
| 14. C3×#125 | C22 | semidirect |
| 30. #808 | C22 | semidirect |
| 31. #807 | C22 | semidirect |
| 32. C4⋊(C3⋊C8) | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 34. #533 | D3 | semidirect |
| 51. C2×D12 | Q8 | semidirect |
| 77. C4⋊Q8 | C2×D3 | semidirect |
| 78. C4⋊Q8 | C2×D3 | semidirect |
| 79. #125 | C2×D3 | semidirect |
| 225. C3 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| C2×C4×D12 | 2 |
| #5087 | 2 |
| #5084 | 2 |
| #5066 | 2 |
| #5001 | 2 |
| #4995 | 2 |
| #4924 | 2 |
| #3077 | 3 |