Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
114 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 22 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. #5391 | C2 | semidirect |
| 3. SL(2,𝔽3)⋊C8 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×SL(2,𝔽3) | 2 |
| #5391 | 2 |
| SL(2,𝔽3)⋊C8 | 2 |
| #1637 | 3 |
| #832 | 4 |