Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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×#97 | C4 | semidirect |
| 13. C4⋊(C3⋊C8) | C4 | semidirect |
| 36. #97 | Dic3 | semidirect |
| 108. C3 | #1300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×M16 | 2 |
| #4932 | 2 |
| #4926 | 2 |
| #1300 | 3 |