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 |
|---|---|---|
| 2. C2×#951 | C2 | semidirect |
| 3. C22×#214 | C2 | semidirect |
| 4. #5516 | C2 | semidirect |
| 5. #5233 | C2 | semidirect |
| 6. #5215 | C2 | semidirect |
| 7. #5075 | C2 | semidirect |
| 8. #5054 | C2 | semidirect |
| 9. #4999 | C2 | semidirect |
| 20. C2×#216 | C22 | semidirect |
| 23. C2×#214 | C22 | semidirect |
| 29. C4×Dic6 | C22 | semidirect |
| 30. #835 | C22 | semidirect |
| 32. #832 | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 59. C2×Dic6 | D4 | semidirect |
| 227. C3 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| C2×#951 | 2 |
| C22×#214 | 2 |
| #5516 | 2 |
| #5233 | 2 |
| #5215 | 2 |
| #5075 | 2 |
| #5054 | 2 |
| #4999 | 2 |
| #3043 | 3 |