Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
276 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 13. #869 | C4 | semidirect |
| 30. C2×C3×C8 | Q8 | semidirect |
| 73. C2×C8 | Dic6 | semidirect |
| 123. C3 | #1993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#869 | 2 |
| C2×C3×#97 | 2 |
| #4936 | 2 |
| #4551 | 2 |
| #1993 | 3 |