Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10590714 | C2 | semidirect |
| 3. C3×#4490 | C2 | semidirect |
| 4. C3×#4489 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. #10589108 | C2 | semidirect |
| 34. #4490 | D3 | semidirect |
| 35. #4489 | D3 | semidirect |
| 274. C32 | #2234 | semidirect |
| 319. C3 | #69323 | semidirect |
| 320. C3 | #69351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592582 | 2 |
| #10590714 | 2 |
| C3×#4490 | 2 |
| C3×#4489 | 2 |
| #10589116 | 2 |
| #10589108 | 2 |
| #69351 | 3 |
| #69323 | 3 |