Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #5215 | C2 | semidirect |
| 4. #5071 | C2 | semidirect |
| 5. #5070 | C2 | semidirect |
| 6. C4×#208 | C2 | semidirect |
| 17. #870 | C22 | semidirect |
| 18. #869 | C22 | semidirect |
| 20. #832 | C22 | semidirect |
| 21. #803 | C22 | semidirect |
| 22. C4×C3⋊C8 | C22 | semidirect |
| 144. C3 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#127 | 2 |
| #5470 | 2 |
| #5215 | 2 |
| #5071 | 2 |
| #5070 | 2 |
| C4×#208 | 2 |
| #3138 | 3 |