Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5094 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 7. #5030 | C2 | semidirect |
| 202. C3 | #3113 | 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 |
| #5094 | 2 |
| #5090 | 2 |
| #5050 | 2 |
| #5043 | 2 |
| #5030 | 2 |
| #4926 | 2 |
| #3113 | 3 |