Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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×#533 | C2 | semidirect |
| 3. #5088 | C2 | semidirect |
| 4. #5085 | C2 | semidirect |
| 5. #5046 | C2 | semidirect |
| 6. #5027 | C2 | semidirect |
| 7. #4925 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 13. C3×C4⋊Q8 | C22 | semidirect |
| 18. C3×C4×Q8 | C22 | semidirect |
| 21. C2×#215 | C22 | semidirect |
| 27. #809 | C22 | semidirect |
| 28. C4⋊(C3⋊C8) | C22 | semidirect |
| 29. C4×C3⋊C8 | C22 | semidirect |
| 30. #533 | D3 | semidirect |
| 70. C4⋊Q8 | C2×D3 | semidirect |
| 71. C4⋊Q8 | C2×D3 | semidirect |
| 80. C4×Q8 | C2×D3 | semidirect |
| 98. C2×C3×C4 | SD16 | semidirect |
| 174. C2×C4 | #215 | semidirect |
| 203. C3 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| C2×#874 | 2 |
| #5088 | 2 |
| #5085 | 2 |
| #5046 | 2 |
| #5027 | 2 |
| #4925 | 2 |
| #3208 | 3 |