Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. C2×#835 | C2 | semidirect |
| 9. C22×C3×Q8 | C4 | semidirect |
| 48. C22×Q8 | Dic3 | semidirect |
| 67. C3×Q8 | C22⋊C4 | semidirect |
| 108. C22×C3 | #103 | semidirect |
| 128. Q8 | #217 | semidirect |
| 153. C22 | #835 | semidirect |
| 164. C3 | #1787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C2×#835 | 2 |
| #5212 | 2 |
| C2×#830 | 2 |
| #1787 | 3 |