Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5516 | C2 | semidirect |
| 5. #5004 | C2 | semidirect |
| 6. C3×H(3,ℤ/4) | C2 | semidirect |
| 7. #4556 | C2 | semidirect |
| 18. C2×Dic12 | C4 | semidirect |
| 19. C2×#204 | C4 | semidirect |
| 32. H(3,ℤ/4) | D3 | semidirect |
| 213. C3 | #1905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| #5516 | 2 |
| #5006 | 2 |
| #5005 | 2 |
| #5004 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #4556 | 2 |
| #1905 | 3 |