Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 232 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 |
|---|---|---|
| 2. C2×C4×SL(2,𝔽3) | C2 | semidirect |
| 3. C2×#859 | C2 | semidirect |
| 8. C2×GL(2,𝔽3) | C4 | semidirect |
| 13. C2×C4×Q8 | D3 | semidirect |
| 61. SL(2,𝔽3) | C22⋊C4 | semidirect |
| 125. Q8 | (C2×D3)⋊C4 | semidirect |
| 144. C2×C4 | GL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×GL(2,𝔽3) | 2 |
| C2×C4×SL(2,𝔽3) | 2 |
| C2×#859 | 2 |
| #1880 | 3 |
| C2×(C2×D3)⋊C4 | 4 |