Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
298 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 22. #835 | C4 | semidirect |
| 82. C3×Q8 | C4⋊C4 | semidirect |
| 160. Q8 | Dic3⋊C4 | semidirect |
| 211. C3 | #1865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| C2×C3×#103 | 2 |
| C2×#835 | 2 |
| #4972 | 2 |
| C2×#808 | 2 |
| #4551 | 2 |
| #4550 | 2 |
| #1865 | 3 |