Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. C2×C3×#103 | C2 | semidirect |
| 4. #5229 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 16. C2×#215 | C4 | semidirect |
| 29. C2×#103 | D3 | semidirect |
| 40. C2×C3×Q8 | C2×C4 | semidirect |
| 69. C2×C3⋊C8 | C2×C4 | semidirect |
| 120. C2×Dic3 | SD16 | semidirect |
| 134. C2×Q8 | C4×D3 | semidirect |
| 258. C3 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#215 | 2 |
| C2×#893 | 2 |
| C2×C3×#103 | 2 |
| #5229 | 2 |
| C2×#821 | 2 |
| #4550 | 2 |
| #4529 | 2 |
| #1877 | 3 |