Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 4. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 72. C2×C3×C4 | M16 | semidirect |
| 131. C2×C4 | #208 | semidirect |
| 162. C3 | #1851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#208 | 2 |
| C3×C4×C22⋊C4 | 2 |
| C2×#830 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4524 | 2 |
| #1851 | 3 |