Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
118 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 118 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. #5386 | C2 | semidirect |
| 3. C8×SL(2,𝔽3) | C2 | semidirect |
| 12. C8×Q8 | D3 | semidirect |
| 42. SL(2,𝔽3) | SD16 | semidirect |
| 72. Q8 | #204 | semidirect |
| 85. C8 | GL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊GL(2,𝔽3) | 2 |
| #5386 | 2 |
| C8×SL(2,𝔽3) | 2 |
| #1666 | 3 |
| C2×#204 | 4 |