Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
186 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 36 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×#101 | C3 | semidirect |
| 33. #101 | A4 | direct (N × H) |
| 66. A4 | #101 | direct (N × H) |
| 101. C22 | C3×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×A4 | 2 |
| A4×M16 | 2 |
| C22×#101 | 3 |
| C3×#101 | 4 |