Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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. #5012 | C2 | semidirect |
| 3. D4⋊(C3⋊C8) | C2 | semidirect |
| 4. #4457 | C2 | semidirect |
| 5. #4455 | C2 | semidirect |
| 54. C3×C8 | M16 | semidirect |
| 92. C8 | #208 | semidirect |
| 106. C3 | #1594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D8 | 2 |
| #5012 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4457 | 2 |
| #4455 | 2 |
| #1594 | 3 |