Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#816 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 17. #924 | C4 | semidirect |
| 42. C2×Dic6 | C2×C4 | semidirect |
| 50. C4⋊Dic3 | C2×C4 | semidirect |
| 130. C22×C3 | #103 | semidirect |
| 188. C22 | #816 | semidirect |
| 202. C3 | #1872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic3 | 2 |
| C2×#924 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#816 | 2 |
| #4551 | 2 |
| #1872 | 3 |