Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1133 conjugacy classes of subgroups; only the 284 normal subgroups are shown.
This group has 1133 conjugacy classes of subgroups — too many to draw. Only its 284 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. C3×#5106 | C2 | semidirect |
| 4. #10591138 | C2 | semidirect |
| 5. #10590688 | C2 | semidirect |
| 10. C2×#3743 | C4 | semidirect |
| 19. C3×#818 | C22 | semidirect |
| 20. C3×#817 | C22 | semidirect |
| 21. #63576 | C22 | semidirect |
| 22. #63574 | C22 | semidirect |
| 27. #5106 | D3 | semidirect |
| 39. C2×C32×C8 | C2×C4 | semidirect |
| 41. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 43. #3743 | C2×C4 | semidirect |
| 72. #818 | C2×D3 | semidirect |
| 73. #817 | C2×D3 | semidirect |
| 115. C2×C3×C8 | C4×D3 | semidirect |
| 210. C2×C8 | #624 | semidirect |
| 240. C32 | #2911 | semidirect |
| 278. C3 | #79177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3743 | 2 |
| #10594969 | 2 |
| C3×#5106 | 2 |
| #10591138 | 2 |
| #10590688 | 2 |
| #79177 | 3 |