Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 1. C2×C3×#127 | C2 | semidirect |
| 2. C22×#213 | C2 | semidirect |
| 3. C2×#874 | C2 | semidirect |
| 4. #5073 | C2 | direct (N × H) |
| 5. C2×C4×C3⋊C8 | C2 | semidirect |
| 12. C3×#127 | C22 | semidirect |
| 15. C2×#213 | C22 | semidirect |
| 18. #874 | C22 | semidirect |
| 19. C4×C3⋊C8 | C22 | semidirect |
| 22. C2×#127 | D3 | semidirect |
| 42. C2×C3⋊C8 | D4 | semidirect |
| 54. #127 | C2×D3 | semidirect |
| 67. C2×C3×C4 | D8 | semidirect |
| 75. C3⋊C8 | C2×D4 | semidirect |
| 105. C3×C4 | C2×D8 | semidirect |
| 120. C2×C4 | #213 | semidirect |
| 127. C2×C3 | #493 | semidirect |
| 140. C4 | C2×#213 | semidirect |
| 143. C3 | C2×#493 | semidirect |
| 146. C2 | #5073 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#127 | 2 |
| C22×#213 | 2 |
| C2×#874 | 2 |
| #5073 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C2×#493 | 3 |