Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5516 | C2 | semidirect |
| 4. C2×#824 | C2 | semidirect |
| 6. C3×H(3,ℤ/4) | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 20. #875 | C4 | semidirect |
| 21. #869 | C4 | semidirect |
| 32. H(3,ℤ/4) | D3 | semidirect |
| 213. C3 | #1912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5526 | 2 |
| #5516 | 2 |
| #5139 | 2 |
| C2×#824 | 2 |
| #5005 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #4531 | 2 |
| #1912 | 3 |