Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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. C3×#423 | C2 | semidirect |
| 3. #4925 | C2 | semidirect |
| 4. #4485 | C2 | semidirect |
| 16. C3×C4⋊C8 | C22 | semidirect |
| 18. C4⋊(C3⋊C8) | C22 | semidirect |
| 22. #423 | D3 | semidirect |
| 56. C4⋊C8 | C2×D3 | semidirect |
| 163. C3 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| C3×#423 | 2 |
| #4925 | 2 |
| #4485 | 2 |
| #1545 | 3 |