Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
210 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. C3×#557 | C2 | semidirect |
| 5. #4547 | C2 | semidirect |
| 6. #4535 | C2 | semidirect |
| 7. #4535 | C2 | semidirect |
| 26. #557 | D3 | semidirect |
| 80. C3×Q8 | SD16 | semidirect |
| 141. Q8 | #215 | semidirect |
| 176. C3 | #1626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| #5088 | 2 |
| #5027 | 2 |
| #4547 | 2 |
| #4535 | 2 |
| #1626 | 3 |