Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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. #5745 | C2 | semidirect |
| 3. C2×C3×#100 | C2 | semidirect |
| 4. C2×#833 | C2 | semidirect |
| 5. #5132 | C2 | semidirect |
| 6. #4745 | C2 | semidirect |
| 7. D3×#100 | C2 | semidirect |
| 19. C2×C3×M16 | C22 | semidirect |
| 20. C2×#208 | C22 | semidirect |
| 22. D3×M16 | C22 | semidirect |
| 24. C3×#100 | C22 | semidirect |
| 25. #833 | C22 | semidirect |
| 26. #824 | C22 | semidirect |
| 27. #823 | C22 | semidirect |
| 34. C2×#100 | D3 | semidirect |
| 85. C2×M16 | C2×D3 | semidirect |
| 89. #100 | C2×D3 | semidirect |
| 231. C3 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1004 | 2 |
| #5745 | 2 |
| C2×C3×#100 | 2 |
| C2×#833 | 2 |
| #5132 | 2 |
| #4745 | 2 |
| D3×#100 | 2 |
| #2888 | 3 |