Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
640 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 469 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. C2×C4⋊(C3⋊C8) | C2 | direct (N × H) |
| 12. C4⋊(C3⋊C8) | C22 | direct (N × H) |
| 18. C22×C3×C4 | C8 | semidirect |
| 43. C2×C3×C4 | C2×C8 | semidirect |
| 53. C22×C4 | C3⋊C8 | semidirect |
| 64. C22×C3 | C4⋊C8 | semidirect |
| 71. C3×C4 | C22×C8 | semidirect |
| 79. C2×C4 | C2×C3⋊C8 | semidirect |
| 88. C2×C3 | C2×C4⋊C8 | semidirect |
| 92. C22 | C4⋊(C3⋊C8) | direct (N × H) |
| 98. C4 | C22×C3⋊C8 | semidirect |
| 102. C3 | C22×C4⋊C8 | semidirect |
| 103. C2 | C2×C4⋊(C3⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C42 | 2 |
| C23×C3⋊C8 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C22×C4⋊C8 | 3 |