Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 121 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. #822 | C4 | direct (N × H) |
| 80. C3×C4 | #108 | semidirect |
| 103. C4 | #822 | direct (N × H) |
| 107. C3 | C4×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×M16 | 2 |
| C2×#822 | 2 |
| C4×#208 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4558 | 2 |
| C4×#108 | 3 |