Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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×#544 | C2 | semidirect |
| 3. #5087 | C2 | semidirect |
| 4. #5084 | C2 | semidirect |
| 5. #5066 | C2 | semidirect |
| 6. #5066 | C2 | semidirect |
| 8. #4999 | C2 | semidirect |
| 9. #4998 | C2 | semidirect |
| 11. #4964 | C2 | semidirect |
| 15. C3×C4⋊Q8 | C22 | semidirect |
| 17. C3×#125 | C22 | semidirect |
| 34. #808 | C22 | semidirect |
| 35. #808 | C22 | semidirect |
| 36. #808 | C22 | semidirect |
| 37. #807 | C22 | semidirect |
| 38. #807 | C22 | semidirect |
| 39. #807 | C22 | semidirect |
| 40. C4⋊(C3⋊C8) | C22 | semidirect |
| 41. C4⋊(C3⋊C8) | C22 | semidirect |
| 42. #544 | D3 | semidirect |
| 59. C2×D12 | Q8 | semidirect |
| 91. C4⋊Q8 | C2×D3 | semidirect |
| 93. #125 | C2×D3 | semidirect |
| 243. C3 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#544 | 2 |
| #5521 | 2 |
| #5087 | 2 |
| #5084 | 2 |
| #5066 | 2 |
| #5001 | 2 |
| #4999 | 2 |
| #4998 | 2 |
| C2×#809 | 2 |
| #4964 | 2 |
| #3081 | 3 |