Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #5118 | C2 | semidirect |
| 5. C4×Dic3⋊C4 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 12. Q8×Dic3 | C4 | semidirect |
| 13. Q8×Dic3 | C4 | semidirect |
| 16. D4×Dic3 | C4 | semidirect |
| 17. D4×Dic3 | C4 | semidirect |
| 101. C3×Q8 | C4⋊C4 | semidirect |
| 105. C3×D4 | C4⋊C4 | semidirect |
| 193. Dic3 | #104 | semidirect |
| 197. Q8 | Dic3⋊C4 | semidirect |
| 201. D4 | Dic3⋊C4 | semidirect |
| 256. C3 | #1806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×#41 | 2 |
| C2×C3×#104 | 2 |
| C2×#837 | 2 |
| #5118 | 2 |
| C4×Dic3⋊C4 | 2 |
| #4555 | 2 |
| #4523 | 2 |
| #1806 | 3 |