Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
283 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 283 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. #557⋊C3 | C2 | direct (N × H) |
| 4. C2×#557 | C3 | semidirect |
| 10. #557 | C2×C3 | semidirect |
| 18. C2×SL(2,𝔽3) | Q8 | semidirect |
| 45. SL(2,𝔽3) | C2×Q8 | semidirect |
| 108. C2 | #557⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #557⋊C3 | 2 |
| C2×C4×SL(2,𝔽3) | 2 |
| C2×#557 | 3 |
| C2×C3×C4⋊C4 | 4 |