Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 4. C2×C4×C3⋊C8 | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 11. C22×C3⋊C8 | C4 | semidirect |
| 16. #830 | C4 | semidirect |
| 31. C3×C22⋊C4 | C8 | semidirect |
| 65. C2×C3×C4 | C2×C8 | semidirect |
| 72. C3⋊C8 | C22⋊C4 | direct (N × H) |
| 89. C22⋊C4 | C3⋊C8 | direct (N × H) |
| 95. C22×C3 | C4×C8 | semidirect |
| 116. C2×C4 | C2×C3⋊C8 | semidirect |
| 133. C22 | C4×C3⋊C8 | semidirect |
| 143. C3 | C8×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊C8 | 2 |
| C3×C4×C22⋊C4 | 2 |
| C2×#830 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4524 | 2 |
| C8×C22⋊C4 | 3 |