Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
122 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 25 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. #4545 | C2 | semidirect |
| 3. #4544 | C2 | semidirect |
| 5. C3×H(5,𝔽2) | C4 | semidirect |
| 9. C3×#100 | C4 | semidirect |
| 28. H(5,𝔽2) | Dic3 | semidirect |
| 33. #100 | Dic3 | semidirect |
| 113. C3 | #1402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#453 | 2 |
| #4545 | 2 |
| #4544 | 2 |
| #1402 | 3 |