Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#204 | C2 | semidirect |
| 3. #5526 | C2 | semidirect |
| 4. #5521 | C2 | semidirect |
| 5. C3×#424 | C2 | semidirect |
| 6. #5120 | C2 | semidirect |
| 7. #5113 | C2 | semidirect |
| 8. #4844 | C2 | semidirect |
| 9. #4841 | C2 | semidirect |
| 27. #875 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 30. C3×C4⋊C8 | C22 | semidirect |
| 31. #821 | C22 | semidirect |
| 32. #816 | C22 | semidirect |
| 33. #816 | C22 | semidirect |
| 40. #424 | D3 | semidirect |
| 96. C4⋊C8 | C2×D3 | semidirect |
| 227. C3 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#908 | 2 |
| C22×#204 | 2 |
| #5526 | 2 |
| #5521 | 2 |
| C3×#424 | 2 |
| #5120 | 2 |
| #5113 | 2 |
| #4844 | 2 |
| #4841 | 2 |
| #3042 | 3 |