Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 61 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. #4680 | C2 | semidirect |
| 5. #4486 | C2 | semidirect |
| 6. #4481 | C2 | semidirect |
| 7. #4457 | C2 | semidirect |
| 80. C3×C8 | SD16 | semidirect |
| 131. C8 | #214 | semidirect |
| 148. C3 | #1671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D4 | 2 |
| #5019 | 2 |
| #5008 | 2 |
| #4680 | 2 |
| #4486 | 2 |
| #4481 | 2 |
| #4457 | 2 |
| #1671 | 3 |