Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 109 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. #4564 | C2 | direct (N × H) |
| 9. C2×C3×Q16 | C4 | semidirect |
| 30. C3×Q16 | C2×C4 | semidirect |
| 41. C2×Q16 | Dic3 | semidirect |
| 73. Q16 | C2×Dic3 | semidirect |
| 105. C2×C3 | #358 | semidirect |
| 118. C3 | C2×#358 | semidirect |
| 119. C2 | #4564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| C2×#818 | 2 |
| C22×C3⋊C16 | 2 |
| #4564 | 2 |
| C2×#358 | 3 |