Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10592894 | C2 | semidirect |
| 3. #10590853 | C2 | semidirect |
| 4. #10590638 | C2 | semidirect |
| 5. C3×#4566 | C2 | semidirect |
| 6. #10589123 | C2 | semidirect |
| 7. #10589109 | C2 | semidirect |
| 12. C2×#3746 | C22 | semidirect |
| 23. #63639 | C22 | semidirect |
| 24. C3×#817 | C22 | semidirect |
| 25. C3×#812 | C22 | semidirect |
| 40. #4566 | D3 | semidirect |
| 112. #817 | C2×D3 | semidirect |
| 117. #812 | C2×D3 | semidirect |
| 399. C32 | #2191 | semidirect |
| 455. C3 | #69253 | semidirect |
| 456. C3 | #72113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5768 | 2 |
| #10592894 | 2 |
| #10590853 | 2 |
| #10590638 | 2 |
| C3×#4566 | 2 |
| #10589123 | 2 |
| #10589109 | 2 |
| #72113 | 3 |
| #69253 | 3 |