Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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. #5516 | C2 | semidirect |
| 3. C3×#410 | C2 | semidirect |
| 4. #5240 | C2 | semidirect |
| 5. #5006 | C2 | semidirect |
| 6. #4740 | C2 | semidirect |
| 11. C2×D3×Q8 | C4 | semidirect |
| 12. C2×#237 | C4 | semidirect |
| 14. C2×#235 | C4 | semidirect |
| 16. C22×Dic6 | C4 | semidirect |
| 31. #410 | D3 | semidirect |
| 221. C3 | #2884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| #5516 | 2 |
| C3×#410 | 2 |
| #5240 | 2 |
| #5006 | 2 |
| #4740 | 2 |
| #2884 | 3 |