Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
114 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 31 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. C3×H(3,ℤ/4) | C2 | semidirect |
| 3. #4553 | C2 | semidirect |
| 8. C2×D24 | C4 | semidirect |
| 10. #817 | C4 | semidirect |
| 14. H(3,ℤ/4) | D3 | semidirect |
| 100. C3 | #1339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5135 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #4553 | 2 |
| #1339 | 3 |