Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
820 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 245 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. C22×C4⋊Dic3 | C2 | semidirect |
| 4. C2×C3⋊#95 | C2 | semidirect |
| 5. C2×C3⋊#95 | C2 | semidirect |
| 6. #4953 | C2 | direct (N × H) |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 19. C3⋊#95 | C22 | semidirect |
| 20. C3⋊#95 | C22 | semidirect |
| 169. C2×C3 | #397 | semidirect |
| 195. C3 | C2×#397 | semidirect |
| 197. C2 | #4953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C22×C4⋊Dic3 | 2 |
| C2×C3⋊#95 | 2 |
| #4953 | 2 |
| C2×#397 | 3 |