Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
296 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 14. C4⋊(C3⋊C8) | C4 | semidirect |
| 16. C4×C3⋊C8 | C4 | semidirect |
| 26. C3×C4⋊C4 | C8 | semidirect |
| 66. C3⋊C8 | C4⋊C4 | direct (N × H) |
| 80. C4⋊C4 | C3⋊C8 | direct (N × H) |
| 92. C3×C4 | C4×C8 | semidirect |
| 126. C4 | C4×C3⋊C8 | semidirect |
| 131. C3 | C8×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C4⋊C4 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4524 | 2 |
| C8×C4⋊C4 | 3 |