Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. Dic3×#41 | C2 | semidirect |
| 3. #5233 | C2 | semidirect |
| 4. #5184 | C2 | semidirect |
| 5. #5164 | C2 | semidirect |
| 6. #5152 | C2 | semidirect |
| 7. #5106 | C2 | semidirect |
| 8. C2×#815 | C2 | semidirect |
| 11. C3×#135 | C4 | semidirect |
| 39. C3×#41 | C2×C4 | semidirect |
| 47. C3×Q16 | C2×C4 | semidirect |
| 48. C3×SD16 | C2×C4 | semidirect |
| 49. C3×D8 | C2×C4 | semidirect |
| 50. C2×C3×C8 | C2×C4 | semidirect |
| 64. #135 | Dic3 | semidirect |
| 104. #41 | C2×Dic3 | semidirect |
| 112. Q16 | C2×Dic3 | semidirect |
| 113. SD16 | C2×Dic3 | semidirect |
| 114. D8 | C2×Dic3 | semidirect |
| 117. C2×C8 | C2×Dic3 | semidirect |
| 174. C3 | #2943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#135 | 2 |
| Dic3×#41 | 2 |
| #5233 | 2 |
| #5184 | 2 |
| #5164 | 2 |
| #5152 | 2 |
| #5106 | 2 |
| C2×#815 | 2 |
| #2943 | 3 |