Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #5521 | C2 | semidirect |
| 3. C3×#418 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. C2×#823 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 15. #940 | C4 | semidirect |
| 28. #418 | D3 | semidirect |
| 39. C2×C3×D4 | C2×C4 | semidirect |
| 54. C3×C4⋊C4 | D4 | semidirect |
| 59. C4⋊Dic3 | D4 | semidirect |
| 62. C4×Dic3 | C2×C4 | semidirect |
| 128. C2×D4 | C4×D3 | semidirect |
| 139. C4⋊C4 | #67 | semidirect |
| 222. C3 | #1887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| #5521 | 2 |
| C3×#418 | 2 |
| #5215 | 2 |
| C2×#823 | 2 |
| #4555 | 2 |
| #4532 | 2 |
| #1887 | 3 |