Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 117 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. C3×C4×C22⋊C4 | C2 | semidirect |
| 3. C4×#217 | C2 | semidirect |
| 5. #4527 | C2 | semidirect |
| 9. C22×C4×D3 | C4 | semidirect |
| 18. C2×(C2×D3)⋊C4 | C4 | semidirect |
| 19. C2×Dic3⋊C4 | C4 | semidirect |
| 21. C2×C4×Dic3 | C4 | semidirect |
| 24. #806 | C4 | direct (N × H) |
| 28. C4×C22⋊C4 | D3 | semidirect |
| 52. C3×C22⋊C4 | C2×C4 | semidirect |
| 57. #217 | C2×C4 | semidirect |
| 94. C22×D3 | C42 | semidirect |
| 119. C2×Dic3 | C42 | semidirect |
| 152. C22⋊C4 | C4×D3 | semidirect |
| 179. C3×C4 | #99 | semidirect |
| 257. C4 | #806 | direct (N × H) |
| 258. C3 | C4×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#67 | 2 |
| C3×C4×C22⋊C4 | 2 |
| C4×#217 | 2 |
| C2×#806 | 2 |
| #4527 | 2 |
| C4×#99 | 3 |