Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C22×C3×M16 | C2 | semidirect |
| 3. C4×#217 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 15. #930 | C4 | semidirect |
| 16. #930 | C4 | semidirect |
| 21. #924 | C4 | semidirect |
| 22. #924 | C4 | semidirect |
| 26. C22×M16 | D3 | semidirect |
| 51. C3×M16 | D4 | semidirect |
| 140. M16 | #67 | semidirect |
| 164. C22×C3 | #104 | semidirect |
| 231. C22 | #825 | semidirect |
| 243. C3 | #1871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| #5791 | 2 |
| C4×#217 | 2 |
| C2×#825 | 2 |
| #4555 | 2 |
| #1871 | 3 |