Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 16. C3×#107 | C4 | semidirect |
| 17. C3×#107 | C4 | semidirect |
| 18. C3×#106 | C4 | semidirect |
| 19. C3×#106 | C4 | semidirect |
| 64. #107 | Dic3 | semidirect |
| 65. #107 | Dic3 | semidirect |
| 66. #106 | Dic3 | semidirect |
| 67. #106 | Dic3 | semidirect |
| 171. C3 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#427 | 2 |
| #4999 | 2 |
| #4997 | 2 |
| #4552 | 2 |
| #4550 | 2 |
| #4532 | 2 |
| #1922 | 3 |