Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
264 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 113 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. #4925 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 4. #4535 | C2 | semidirect |
| 5. D4⋊(C3⋊C8) | C2 | semidirect |
| 30. C3×#41 | C8 | semidirect |
| 77. C3×Q8 | C2×C8 | semidirect |
| 80. C3×D4 | C2×C8 | semidirect |
| 102. #41 | C3⋊C8 | semidirect |
| 150. Q8 | C2×C3⋊C8 | semidirect |
| 153. D4 | C2×C3⋊C8 | semidirect |
| 197. C3 | #1477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41 | 2 |
| #4925 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4535 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #1477 | 3 |