Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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. C4×#235 | C2 | semidirect |
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 4. #5113 | C2 | semidirect |
| 5. #5106 | C2 | semidirect |
| 6. C4×Dic12 | C2 | semidirect |
| 7. C4×D24 | C2 | semidirect |
| 8. C4×#204 | C2 | semidirect |
| 17. #904 | C4 | direct (N × H) |
| 37. C2×C4×C8 | D3 | semidirect |
| 42. #235 | C2×C4 | semidirect |
| 48. C2×C3×C8 | C2×C4 | semidirect |
| 61. Dic12 | C2×C4 | semidirect |
| 62. D24 | C2×C4 | semidirect |
| 63. #204 | C2×C4 | semidirect |
| 118. C2×C8 | C4×D3 | semidirect |
| 138. C3×C4 | #135 | semidirect |
| 177. C4 | #904 | direct (N × H) |
| 180. C3 | C4×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C4×#235 | 2 |
| C2×C3×C4×C8 | 2 |
| #5113 | 2 |
| #5106 | 2 |
| C4×Dic12 | 2 |
| C4×D24 | 2 |
| C4×#204 | 2 |
| C4×#135 | 3 |