Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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. #5240 | C2 | semidirect |
| 3. #5236 | C2 | semidirect |
| 4. #5234 | C2 | semidirect |
| 5. #5233 | C2 | semidirect |
| 8. C3×2−1+4 | C4 | semidirect |
| 11. C3×H(5,𝔽2) | C4 | semidirect |
| 16. #926 | C22 | semidirect |
| 17. C2×#208 | C22 | semidirect |
| 18. C22×C3⋊C8 | C22 | semidirect |
| 65. 2−1+4 | Dic3 | semidirect |
| 68. H(5,𝔽2) | Dic3 | semidirect |
| 211. C3 | #1794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#585 | 2 |
| #5240 | 2 |
| #5236 | 2 |
| #5234 | 2 |
| #5233 | 2 |
| #1794 | 3 |