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 |
|---|---|---|
| 1. C3×#536 | C2 | semidirect |
| 3. C22×#215 | C2 | semidirect |
| 4. #5521 | C2 | semidirect |
| 5. #5233 | C2 | semidirect |
| 6. #5225 | C2 | semidirect |
| 7. #5083 | C2 | semidirect |
| 8. #5057 | C2 | semidirect |
| 9. #4999 | C2 | semidirect |
| 14. C3×C4⋊Q8 | C22 | semidirect |
| 15. C3×#124 | C22 | semidirect |
| 30. #835 | C22 | semidirect |
| 31. #835 | C22 | semidirect |
| 32. #832 | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 36. #536 | D3 | semidirect |
| 87. C4⋊Q8 | C2×D3 | semidirect |
| 88. #124 | 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 |
|---|---|
| C3×#536 | 2 |
| C2×#949 | 2 |
| C22×#215 | 2 |
| #5521 | 2 |
| #5233 | 2 |
| #5225 | 2 |
| #5083 | 2 |
| #5057 | 2 |
| #4999 | 2 |
| #3042 | 3 |