Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 250 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 |
|---|---|---|
| 2. #5070 | C2 | semidirect |
| 3. #5031 | C2 | semidirect |
| 4. #5007 | C2 | semidirect |
| 5. #4544 | C2 | semidirect |
| 6. #4535 | C2 | semidirect |
| 7. D4⋊(C3⋊C8) | C2 | semidirect |
| 193. C3 | #1641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#550 | 2 |
| #5070 | 2 |
| #5031 | 2 |
| #5007 | 2 |
| #4544 | 2 |
| #4535 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #1641 | 3 |