Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#1007 | C2 | semidirect |
| 2. C2×#947 | C2 | semidirect |
| 3. C2×#908 | C2 | semidirect |
| 4. C2×C3×#101 | C2 | semidirect |
| 5. C2×#825 | C2 | semidirect |
| 6. #4753 | C2 | direct (N × H) |
| 11. #1007 | C22 | semidirect |
| 19. #947 | C22 | semidirect |
| 23. #908 | C22 | semidirect |
| 26. C3×#101 | C22 | semidirect |
| 27. #825 | C22 | semidirect |
| 33. C2×#101 | D3 | semidirect |
| 90. #101 | C2×D3 | semidirect |
| 209. C2×C3 | #454 | semidirect |
| 228. C3 | C2×#454 | semidirect |
| 233. C2 | #4753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1007 | 2 |
| C2×#947 | 2 |
| C2×#908 | 2 |
| C2×C3×#101 | 2 |
| C2×#825 | 2 |
| #4753 | 2 |
| C2×#454 | 3 |