Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 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×#810 | C2 | direct (N × H) |
| 11. C22×Dic6 | C4 | semidirect |
| 17. #810 | C22 | direct (N × H) |
| 34. C2×Dic6 | C2×C4 | semidirect |
| 67. Dic6 | C22×C4 | semidirect |
| 87. C22×C3 | #103 | semidirect |
| 114. C2×C3 | C2×#103 | semidirect |
| 118. C22 | #810 | direct (N × H) |
| 128. C3 | C22×#103 | semidirect |
| 129. C2 | C2×#810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#810 | 2 |
| C22×#103 | 3 |