Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. C2×C4×Dic6 | C2 | semidirect |
| 3. #5063 | C2 | semidirect |
| 4. #5054 | C2 | semidirect |
| 5. #5050 | C2 | semidirect |
| 6. #5044 | C2 | semidirect |
| 9. #5030 | C2 | semidirect |
| 10. #5018 | C2 | semidirect |
| 11. #4926 | C2 | semidirect |
| 257. C3 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#529 | 2 |
| C2×C4×Dic6 | 2 |
| #5063 | 2 |
| #5054 | 2 |
| #5050 | 2 |
| #5044 | 2 |
| #5040 | 2 |
| #5034 | 2 |
| #5030 | 2 |
| #5018 | 2 |
| #4926 | 2 |
| #3117 | 3 |