Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 177. C3 | #2097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#106 | 2 |
| C2×#816 | 2 |
| #4977 | 2 |
| #4973 | 2 |
| C2×#810 | 2 |
| C2×#807 | 2 |
| #4550 | 2 |
| #2097 | 3 |