Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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×#951 | C2 | semidirect |
| 3. C2×#924 | C2 | semidirect |
| 4. #5239 | C2 | semidirect |
| 5. #5232 | C2 | semidirect |
| 6. #5228 | C2 | semidirect |
| 7. #5218 | C2 | semidirect |
| 8. #5207 | C2 | semidirect |
| 20. C22×Dic6 | C22 | semidirect |
| 23. C2×#216 | C22 | semidirect |
| 24. C2×#214 | C22 | semidirect |
| 25. C2×C4⋊Dic3 | C22 | semidirect |
| 29. #924 | C22 | semidirect |
| 31. C2×#208 | C22 | semidirect |
| 32. #835 | C22 | semidirect |
| 33. #832 | C22 | semidirect |
| 35. #830 | C22 | semidirect |
| 208. C22×C3 | #137 | semidirect |
| 275. C22 | #951 | semidirect |
| 285. C3 | #3007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C2×#951 | 2 |
| C2×#924 | 2 |
| #5239 | 2 |
| #5232 | 2 |
| #5228 | 2 |
| #5218 | 2 |
| #5207 | 2 |
| #3007 | 3 |