Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #5076 | C2 | semidirect |
| 3. #5070 | C2 | semidirect |
| 4. #4682 | C2 | semidirect |
| 5. C8×C3⋊C8 | C2 | semidirect |
| 51. C3×C8 | SD16 | semidirect |
| 53. C3⋊C8 | D8 | semidirect |
| 85. C8 | #214 | semidirect |
| 98. C3 | #1706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#493 | 2 |
| #5076 | 2 |
| #5070 | 2 |
| #4682 | 2 |
| C8×C3⋊C8 | 2 |
| #1706 | 3 |