Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#817 | C2 | semidirect |
| 3. C2×#812 | C2 | semidirect |
| 4. #4566 | C2 | direct (N × H) |
| 9. C3×#135 | C4 | semidirect |
| 11. C2×C3×Q16 | C4 | semidirect |
| 13. C2×C3×D8 | C4 | semidirect |
| 17. #817 | C22 | semidirect |
| 19. #812 | C22 | semidirect |
| 36. C3×Q16 | C2×C4 | semidirect |
| 40. C3×D8 | C2×C4 | semidirect |
| 53. #135 | Dic3 | semidirect |
| 55. C2×Q16 | Dic3 | semidirect |
| 57. C2×D8 | Dic3 | semidirect |
| 99. Q16 | C2×Dic3 | semidirect |
| 103. D8 | C2×Dic3 | semidirect |
| 151. C2×C3 | #360 | semidirect |
| 165. C3 | C2×#360 | semidirect |
| 169. C2 | #4566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#135 | 2 |
| C2×#817 | 2 |
| C2×#812 | 2 |
| #4566 | 2 |
| C2×#360 | 3 |