Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#214 | C2 | semidirect |
| 3. C2×#909 | C2 | semidirect |
| 4. #5516 | C2 | semidirect |
| 5. C3×#418 | C2 | semidirect |
| 6. #5119 | C2 | semidirect |
| 7. #5002 | C2 | semidirect |
| 8. #4767 | C2 | semidirect |
| 9. #4762 | C2 | semidirect |
| 25. C2×Dic12 | C22 | semidirect |
| 26. C2×#204 | C22 | semidirect |
| 27. #887 | C22 | semidirect |
| 31. Dic3⋊C8 | C22 | semidirect |
| 32. #810 | C22 | semidirect |
| 33. #809 | C22 | semidirect |
| 41. #418 | D3 | semidirect |
| 58. 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 |
|---|---|
| #5805 | 2 |
| C22×#214 | 2 |
| C2×#909 | 2 |
| #5516 | 2 |
| C3×#418 | 2 |
| #5119 | 2 |
| #5002 | 2 |
| #4767 | 2 |
| #4762 | 2 |
| #3043 | 3 |