Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 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. #4455 | C2 | semidirect |
| 5. C8×C3⋊C8 | C2 | semidirect |
| 26. C3×M16 | C8 | semidirect |
| 57. C3×C8 | C2×C8 | semidirect |
| 60. C3⋊C8 | M16 | direct (N × H) |
| 64. M16 | C3⋊C8 | direct (N × H) |
| 97. C8 | C2×C3⋊C8 | semidirect |
| 112. C3 | C8×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×M16 | 2 |
| #4925 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4455 | 2 |
| C8×C3⋊C8 | 2 |
| C8×M16 | 3 |