Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
363 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. #5409 | C2 | direct (N × H) |
| 3. C2×A4⋊C8 | C2 | semidirect |
| 11. A4⋊C8 | C22 | semidirect |
| 54. C2×A4 | M16 | semidirect |
| 110. A4 | C2×M16 | semidirect |
| 130. C23 | #208 | semidirect |
| 179. C22 | C2×#208 | semidirect |
| 194. C2 | #5409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×A4 | 2 |
| #5409 | 2 |
| C2×A4⋊C8 | 2 |
| C2×#407 | 3 |
| C2×#208 | 4 |