Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
996 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 996 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. C22×#214 | C2 | semidirect |
| 3. C2×#924 | C2 | semidirect |
| 4. #5218 | C2 | direct (N × H) |
| 5. C2×#832 | C2 | semidirect |
| 6. C2×#830 | C2 | semidirect |
| 15. C22×Dic6 | C22 | semidirect |
| 18. C2×#214 | C22 | semidirect |
| 19. C2×C4⋊Dic3 | C22 | semidirect |
| 21. #924 | C22 | semidirect |
| 23. C22×C3⋊C8 | C22 | semidirect |
| 24. #832 | C22 | semidirect |
| 25. #830 | C22 | semidirect |
| 55. C2×Dic6 | C23 | semidirect |
| 59. C4⋊Dic3 | C23 | semidirect |
| 62. C2×C3⋊C8 | C23 | semidirect |
| 91. C23×C3 | SD16 | semidirect |
| 153. C22×C3 | C2×SD16 | semidirect |
| 171. C23 | #214 | semidirect |
| 194. C2×C3 | #450 | semidirect |
| 208. C22 | C2×#214 | semidirect |
| 216. C3 | C2×#450 | semidirect |
| 219. C2 | #5218 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C22×#214 | 2 |
| C2×#924 | 2 |
| #5218 | 2 |
| C2×#832 | 2 |
| C2×#830 | 2 |
| C2×#450 | 3 |