Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
816 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 389 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×#835 | C2 | direct (N × H) |
| 8. C22×C3×Q8 | C4 | semidirect |
| 17. #835 | C22 | direct (N × H) |
| 26. C2×C3×Q8 | C2×C4 | semidirect |
| 42. C22×Q8 | Dic3 | semidirect |
| 58. C3×Q8 | C22×C4 | semidirect |
| 73. C2×Q8 | C2×Dic3 | semidirect |
| 87. C22×C3 | #103 | semidirect |
| 103. Q8 | C22×Dic3 | semidirect |
| 114. C2×C3 | C2×#103 | semidirect |
| 118. C22 | #835 | direct (N × H) |
| 128. C3 | C22×#103 | semidirect |
| 129. C2 | C2×#835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C22×C4⋊Dic3 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#835 | 2 |
| C22×#103 | 3 |