Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 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×#948 | C2 | direct (N × H) |
| 3. C22×#208 | C2 | semidirect |
| 4. C23×C3⋊C8 | C2 | semidirect |
| 11. #948 | C22 | direct (N × H) |
| 12. C2×#208 | C22 | semidirect |
| 15. C22×C3⋊C8 | C22 | semidirect |
| 29. #208 | C23 | semidirect |
| 32. C2×C3⋊C8 | C23 | semidirect |
| 69. C22×C3 | #131 | semidirect |
| 88. C2×C3 | C2×#131 | semidirect |
| 91. C22 | #948 | direct (N × H) |
| 97. C3 | C22×#131 | semidirect |
| 99. C2 | C2×#948 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C2×#948 | 2 |
| C22×#208 | 2 |
| C23×C3⋊C8 | 2 |
| C22×#131 | 3 |