Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
222 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #5119 | C2 | semidirect |
| 5. C2×#815 | C2 | semidirect |
| 6. C3×#341 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 17. #821 | C4 | semidirect |
| 19. #816 | C4 | semidirect |
| 27. #341 | D3 | semidirect |
| 175. C3 | #1938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#825 | 2 |
| #5129 | 2 |
| #5119 | 2 |
| #5113 | 2 |
| C2×#815 | 2 |
| C3×#341 | 2 |
| #4555 | 2 |
| #1938 | 3 |