Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 77 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×#407 | C2 | semidirect |
| 3. #5207 | C2 | semidirect |
| 4. #4469 | C2 | semidirect |
| 5. #4468 | C2 | semidirect |
| 26. #407 | D3 | semidirect |
| 88. C22×D3 | M16 | semidirect |
| 107. C2×Dic3 | M16 | semidirect |
| 236. C3 | #1465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#67 | 2 |
| C3×#407 | 2 |
| #5207 | 2 |
| #4469 | 2 |
| #4468 | 2 |
| #1465 | 3 |