Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 208 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 |
|---|---|---|
| 175. C3 | #2064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#108 | 2 |
| C2×#824 | 2 |
| #5121 | 2 |
| #5120 | 2 |
| C2×#816 | 2 |
| #5102 | 2 |
| #4554 | 2 |
| #2064 | 3 |