Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 42 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. C22×#106 | C3 | semidirect |
| 6. C8×A4 | C4 | semidirect |
| 24. C22×C8 | C3×C4 | semidirect |
| 31. #106 | A4 | direct (N × H) |
| 59. A4 | #106 | direct (N × H) |
| 84. C8 | C4×A4 | semidirect |
| 94. C22 | C3×#106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×A4 | 2 |
| A4×C4⋊C4 | 2 |
| C22×#106 | 3 |
| C3×#106 | 4 |