Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5229 | C2 | semidirect |
| 4. C2×#835 | C2 | semidirect |
| 6. #4551 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 14. C2×C3×SD16 | C4 | semidirect |
| 40. C2×C3×Q8 | C2×C4 | semidirect |
| 59. C2×C3×C8 | C2×C4 | semidirect |
| 75. C2×SD16 | Dic3 | semidirect |
| 125. C2×Dic3 | SD16 | semidirect |
| 134. C2×Q8 | C2×Dic3 | semidirect |
| 156. C2×C8 | C2×Dic3 | 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×C3×SD16 | 2 |
| C2×D4×Dic3 | 2 |
| #5229 | 2 |
| C2×#835 | 2 |
| C2×#832 | 2 |
| #4551 | 2 |
| #4550 | 2 |
| #1877 | 3 |