Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 72. C3×C8 | Q16 | semidirect |
| 111. C8 | Dic12 | semidirect |
| 123. C3 | #1723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4699 | 2 |
| #4682 | 2 |
| #4681 | 2 |
| #4680 | 2 |
| C3×#322 | 2 |
| #1723 | 3 |