Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5083 | C2 | semidirect |
| 6. #5044 | C2 | semidirect |
| 7. #5026 | C2 | semidirect |
| 8. #4926 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 13. C3×C4⋊Q8 | C22 | semidirect |
| 18. C3×C4×Q8 | C22 | semidirect |
| 28. #835 | C22 | semidirect |
| 31. #807 | C22 | semidirect |
| 32. C4⋊(C3⋊C8) | C22 | semidirect |
| 33. #803 | C22 | semidirect |
| 34. #533 | D3 | semidirect |
| 76. C4⋊Q8 | C2×D3 | semidirect |
| 77. C4⋊Q8 | C2×D3 | semidirect |
| 82. C4×Q8 | C2×D3 | semidirect |
| 219. C3 | #3110 | 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 |
| #5083 | 2 |
| #5046 | 2 |
| #5044 | 2 |
| #5026 | 2 |
| #4926 | 2 |
| #3110 | 3 |