Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5470 | C2 | semidirect |
| 3. #5069 | C2 | semidirect |
| 4. #5064 | C2 | semidirect |
| 5. #5060 | C2 | semidirect |
| 6. #5055 | C2 | semidirect |
| 7. #5052 | C2 | semidirect |
| 9. C4×#216 | C2 | semidirect |
| 10. C4×#214 | C2 | semidirect |
| 11. C4×#208 | C2 | semidirect |
| 253. C3 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#529 | 2 |
| #5470 | 2 |
| #5069 | 2 |
| #5064 | 2 |
| #5060 | 2 |
| #5055 | 2 |
| #5052 | 2 |
| #5042 | 2 |
| C4×#216 | 2 |
| C4×#214 | 2 |
| C4×#208 | 2 |
| #3172 | 3 |