Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 135. C3 | #1684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q8 | 2 |
| #5021 | 2 |
| #5020 | 2 |
| #4681 | 2 |
| #4482 | 2 |
| #4481 | 2 |
| #4458 | 2 |
| #1684 | 3 |