Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
150 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 77. C3×C8 | Q16 | semidirect |
| 123. C8 | #216 | semidirect |
| 137. C3 | #1672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q8 | 2 |
| #5031 | 2 |
| #5021 | 2 |
| #4680 | 2 |
| #4486 | 2 |
| #4481 | 2 |
| #4457 | 2 |
| #1672 | 3 |