Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
293 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 293 conjugacy classes of subgroups — too many to draw. Only its 56 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×#4557 | C2 | semidirect |
| 3. C3×#4553 | C2 | semidirect |
| 8. C2×#3745 | C4 | semidirect |
| 11. #63644 | C4 | semidirect |
| 18. #4557 | D3 | semidirect |
| 19. #4553 | D3 | semidirect |
| 209. C32 | #1339 | semidirect |
| 247. C3 | #67481 | semidirect |
| 248. C3 | #67534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592834 | 2 |
| C3×#4557 | 2 |
| C3×#4553 | 2 |
| #67534 | 3 |
| #67481 | 3 |