Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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. C2×C3×#137 | C2 | semidirect |
| 3. #5812 | C2 | semidirect |
| 4. C22×#215 | C2 | semidirect |
| 5. #5233 | C2 | semidirect |
| 6. #5185 | C2 | semidirect |
| 7. #5163 | C2 | semidirect |
| 8. #5131 | C2 | semidirect |
| 9. #5119 | C2 | semidirect |
| 15. C2×C3×Q16 | C22 | semidirect |
| 16. C2×C3×SD16 | C22 | semidirect |
| 20. Q8×Dic3 | C22 | semidirect |
| 30. #835 | C22 | semidirect |
| 31. #832 | C22 | semidirect |
| 33. Dic3⋊C8 | C22 | semidirect |
| 34. C2×#137 | D3 | semidirect |
| 48. C2×C3×Q8 | D4 | semidirect |
| 81. C2×Q16 | C2×D3 | semidirect |
| 84. C2×SD16 | C2×D3 | semidirect |
| 134. C2×Q8 | #67 | semidirect |
| 227. C3 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| #5830 | 2 |
| #5812 | 2 |
| C22×#215 | 2 |
| #5233 | 2 |
| #5185 | 2 |
| #5163 | 2 |
| #5131 | 2 |
| #5119 | 2 |
| #3043 | 3 |