Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
148 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 128. C3 | #2103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5124 | 2 |
| #4999 | 2 |
| C3×#344 | 2 |
| C3⋊#338 | 2 |
| #4558 | 2 |
| #4533 | 2 |
| #2103 | 3 |