Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
155 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 155 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 |
|---|---|---|
| 6. C8×A4 | C4 | semidirect |
| 23. C22×C8 | Dic3 | semidirect |
| 59. A4 | #107 | semidirect |
| 86. C8 | SL(2,ℤ/4) | semidirect |
| 100. C22 | #818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×A4 | 2 |
| C4⋊SL(2,ℤ/4) | 2 |
| #1808 | 3 |
| #818 | 4 |