Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×C3×#97 | C2 | semidirect |
| 4. C2×#815 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 19. C2×D3×C8 | C4 | semidirect |
| 22. (C2×D3)⋊C8 | C4 | semidirect |
| 27. C2×#97 | D3 | semidirect |
| 101. C3×C8 | C22⋊C4 | semidirect |
| 142. C2×D3 | #97 | semidirect |
| 178. C8 | (C2×D3)⋊C4 | semidirect |
| 202. C3 | #1752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×C3×#97 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#815 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4550 | 2 |
| #4524 | 2 |
| #1752 | 3 |