Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
175 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 175 conjugacy classes of subgroups — too many to draw. Only its 46 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. C4×SL(2,𝔽3) | C4 | semidirect |
| 22. C4×Q8 | Dic3 | semidirect |
| 38. SL(2,𝔽3) | C4⋊C4 | semidirect |
| 74. Q8 | C4⋊Dic3 | semidirect |
| 111. C4 | #859 | semidirect |
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 |
| #1803 | 3 |
| C2×C4⋊Dic3 | 4 |