Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #5091 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 103. C2×C3×C4 | Q16 | semidirect |
| 176. C2×C4 | #216 | semidirect |
| 202. C3 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| C2×C4×Dic6 | 2 |
| #5091 | 2 |
| #5090 | 2 |
| #5050 | 2 |
| #5044 | 2 |
| C4×#216 | 2 |
| #4925 | 2 |
| #3104 | 3 |