Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×C3×Q16 | C4 | semidirect |
| 72. C2×Q16 | Dic3 | semidirect |
| 118. C2×Dic3 | Q16 | semidirect |
| 231. C3 | #1878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| C2×Q8×Dic3 | 2 |
| #5229 | 2 |
| C2×#835 | 2 |
| #4551 | 2 |
| #4550 | 2 |
| #1878 | 3 |