Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
235 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 3. #5391 | C2 | direct (N × H) |
| 18. C2×SL(2,𝔽3) | Q8 | semidirect |
| 41. SL(2,𝔽3) | C2×Q8 | semidirect |
| 99. C2 | #5391 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×SL(2,𝔽3) | 2 |
| C2×#859 | 2 |
| #5391 | 2 |
| C2×#477 | 3 |
| C2×C4⋊Dic3 | 4 |