Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
394 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 96 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. C22×C4×Q8 | C3 | semidirect |
| 5. Q8×A4 | C4 | direct (N × H) |
| 21. C4×A4 | Q8 | direct (N × H) |
| 27. C22×Q8 | C3×C4 | semidirect |
| 37. C4×Q8 | A4 | direct (N × H) |
| 71. C22×C4 | C3×Q8 | semidirect |
| 82. A4 | C4×Q8 | direct (N × H) |
| 95. Q8 | C4×A4 | direct (N × H) |
| 127. C22 | C3×C4×Q8 | semidirect |
| 134. C4 | Q8×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×A4 | 2 |
| A4×C4⋊C4 | 2 |
| C42×A4 | 2 |
| C22×C4×Q8 | 3 |
| C3×C4×Q8 | 4 |