Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 4. Dic3×C22⋊C4 | C2 | semidirect |
| 5. #4527 | C2 | semidirect |
| 8. C23×Dic3 | C4 | semidirect |
| 11. C2×#217 | C4 | semidirect |
| 16. C2×C4⋊Dic3 | C4 | semidirect |
| 18. C2×C4×Dic3 | C4 | semidirect |
| 19. C3×#99 | C4 | semidirect |
| 20. #834 | C4 | semidirect |
| 47. C3×C22⋊C4 | C2×C4 | semidirect |
| 51. #217 | C2×C4 | semidirect |
| 69. #99 | Dic3 | direct (N × H) |
| 77. C23×C3 | C42 | semidirect |
| 90. C2×C3×C4 | C42 | semidirect |
| 132. C22⋊C4 | C2×Dic3 | semidirect |
| 160. Dic3 | #99 | direct (N × H) |
| 167. C23 | C4×Dic3 | semidirect |
| 196. C2×C4 | C4×Dic3 | semidirect |
| 230. C3 | C4×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic3 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| Dic3×C22⋊C4 | 2 |
| #4527 | 2 |
| C4×#99 | 3 |