Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C3×SD16 | C2 | semidirect |
| 2. C2×#947 | C2 | semidirect |
| 3. C22×#215 | C2 | semidirect |
| 4. C2×#940 | C2 | semidirect |
| 5. C22×#213 | C2 | semidirect |
| 6. C22×D24 | C2 | semidirect |
| 7. #5176 | C2 | direct (N × H) |
| 8. C2×#815 | C2 | semidirect |
| 16. C2×C3×SD16 | C22 | semidirect |
| 19. #947 | C22 | semidirect |
| 21. C2×#215 | C22 | semidirect |
| 23. #940 | C22 | semidirect |
| 25. C2×#213 | C22 | semidirect |
| 30. C2×D24 | C22 | semidirect |
| 31. #815 | C22 | semidirect |
| 33. C22×SD16 | D3 | semidirect |
| 65. C2×C3×C8 | D4 | semidirect |
| 72. C2×C3⋊C8 | D4 | semidirect |
| 83. C2×SD16 | C2×D3 | semidirect |
| 128. C3×C8 | C2×D4 | semidirect |
| 129. C3⋊C8 | C2×D4 | semidirect |
| 160. C2×C8 | #67 | semidirect |
| 214. C8 | C2×#67 | semidirect |
| 216. C2×C3 | #496 | semidirect |
| 238. C3 | C2×#496 | semidirect |
| 242. C2 | #5176 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×SD16 | 2 |
| C2×#947 | 2 |
| C22×#215 | 2 |
| C2×#940 | 2 |
| C22×#213 | 2 |
| C22×D24 | 2 |
| #5176 | 2 |
| C2×#815 | 2 |
| C2×#496 | 3 |