Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 197 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. #5092 | C2 | direct (N × H) |
| 60. C2×C3×C4 | Q16 | semidirect |
| 92. C3×C4 | C2×Q16 | semidirect |
| 104. C2×C4 | #216 | semidirect |
| 110. C2×C3 | #494 | semidirect |
| 119. C4 | C2×#216 | semidirect |
| 121. C3 | C2×#494 | semidirect |
| 122. C2 | #5092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| C22×#216 | 2 |
| C2×#869 | 2 |
| #5092 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C2×#494 | 3 |