Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 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×#353 | C2 | semidirect |
| 3. #4545 | C2 | semidirect |
| 8. #874 | C4 | semidirect |
| 11. C4×C3⋊C8 | C4 | semidirect |
| 14. #353 | D3 | semidirect |
| 99. C3 | #1408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5073 | 2 |
| C3×#353 | 2 |
| #4545 | 2 |
| #1408 | 3 |