Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1032 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 151 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. #10592536 | C2 | semidirect |
| 3. #10592532 | C2 | semidirect |
| 4. C32×#331 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589351 | C2 | semidirect |
| 7. #10589351 | C2 | semidirect |
| 19. C32×C4⋊C8 | C22 | semidirect |
| 20. C32×C4⋊C8 | C22 | semidirect |
| 24. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 25. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 29. C3×#331 | D3 | semidirect |
| 71. C3×C4⋊C8 | C2×D3 | semidirect |
| 72. C3×C4⋊C8 | C2×D3 | semidirect |
| 118. #331 | C3⋊D3 | semidirect |
| 178. C4⋊C8 | C2×C3⋊D3 | semidirect |
| 179. C4⋊C8 | C2×C3⋊D3 | semidirect |
| 268. C32 | #1545 | semidirect |
| 328. C3 | #68383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#127 | 2 |
| #10592536 | 2 |
| #10592532 | 2 |
| C32×#331 | 2 |
| #10589410 | 2 |
| #10589351 | 2 |
| #68383 | 3 |