Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 8. C3×C4⋊Q8 | C4 | semidirect |
| 39. C4⋊Q8 | Dic3 | semidirect |
| 84. C3×C4 | #103 | semidirect |
| 116. C4 | #835 | semidirect |
| 119. C3 | #1956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| C2×#835 | 2 |
| #4935 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #1956 | 3 |