Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
146 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 76. C3×C8 | Q16 | semidirect |
| 123. C8 | #216 | semidirect |
| 137. C3 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#498 | 2 |
| #5091 | 2 |
| #5090 | 2 |
| #4679 | 2 |
| #4547 | 2 |
| #4546 | 2 |
| #4458 | 2 |
| #1692 | 3 |