Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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×Dic12 | C2 | semidirect |
| 4. C2×C3×#107 | C2 | semidirect |
| 5. C2×#810 | C2 | semidirect |
| 6. #4887 | C2 | direct (N × H) |
| 16. C2×Dic12 | C22 | semidirect |
| 21. C3×#107 | C22 | semidirect |
| 22. #810 | C22 | semidirect |
| 27. C2×#107 | D3 | semidirect |
| 65. #107 | C2×D3 | semidirect |
| 70. C22×D3 | Q16 | semidirect |
| 120. C2×D3 | C2×Q16 | semidirect |
| 150. C2×C3 | #467 | semidirect |
| 169. C3 | C2×#467 | semidirect |
| 171. C2 | #4887 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic12 | 2 |
| C22×D3×C8 | 2 |
| C2×#897 | 2 |
| C2×C3×#107 | 2 |
| C2×#810 | 2 |
| #4887 | 2 |
| C2×#467 | 3 |