Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
384 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. #10590284 | C2 | semidirect |
| 4. #10590254 | C2 | semidirect |
| 6. #10589097 | C2 | semidirect |
| 7. #10589095 | C2 | semidirect |
| 301. C32 | #1678 | semidirect |
| 347. C3 | #68410 | semidirect |
| 348. C3 | #71208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592774 | 2 |
| C3×#5070 | 2 |
| #10590284 | 2 |
| #10590254 | 2 |
| C3×#4544 | 2 |
| #10589097 | 2 |
| #10589095 | 2 |
| #71208 | 3 |
| #68410 | 3 |