Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
670 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5220 | C2 | semidirect |
| 3. C2×#834 | C2 | semidirect |
| 6. C3×H(5,𝔽2) | C4 | semidirect |
| 10. C23×Dic3 | C22 | semidirect |
| 12. C2×#217 | C22 | semidirect |
| 39. H(5,𝔽2) | Dic3 | semidirect |
| 57. C23×C3 | C22⋊C4 | semidirect |
| 68. C2×C3×C4 | C22⋊C4 | semidirect |
| 120. C23 | #217 | semidirect |
| 137. C2×C4 | #217 | semidirect |
| 160. C3 | #1790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| #5220 | 2 |
| C2×#834 | 2 |
| #1790 | 3 |