Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×#131 | C2 | semidirect |
| 3. #5825 | C2 | semidirect |
| 4. C22×#204 | C2 | semidirect |
| 5. #5134 | C2 | semidirect |
| 6. #5131 | C2 | semidirect |
| 7. #5120 | C2 | semidirect |
| 8. #5114 | C2 | semidirect |
| 9. #5106 | C2 | semidirect |
| 16. C2×C3×M16 | C22 | semidirect |
| 18. C22×C3×C8 | C22 | semidirect |
| 28. #924 | C22 | semidirect |
| 33. #818 | C22 | semidirect |
| 34. #817 | C22 | semidirect |
| 35. #816 | C22 | semidirect |
| 37. C2×#131 | D3 | semidirect |
| 66. C2×C3×C8 | D4 | semidirect |
| 89. C2×M16 | C2×D3 | semidirect |
| 91. C22×C8 | C2×D3 | semidirect |
| 158. C2×C8 | #67 | semidirect |
| 235. C3 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| #5830 | 2 |
| #5825 | 2 |
| C22×#204 | 2 |
| #5134 | 2 |
| #5131 | 2 |
| #5120 | 2 |
| #5114 | 2 |
| #5106 | 2 |
| #3057 | 3 |