Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
461 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 461 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. C3×#5195 | C2 | semidirect |
| 3. #10590854 | C2 | semidirect |
| 4. #10590636 | C2 | semidirect |
| 5. #10589432 | C2 | semidirect |
| 6. #10589124 | C2 | semidirect |
| 7. #10589109 | C2 | semidirect |
| 17. C2×C3×Dic12 | C22 | semidirect |
| 21. #63644 | C22 | semidirect |
| 22. #63639 | C22 | semidirect |
| 25. C3×#812 | C22 | semidirect |
| 33. #5195 | D3 | semidirect |
| 98. C2×Dic12 | C2×D3 | semidirect |
| 118. #812 | C2×D3 | semidirect |
| 393. C32 | #2191 | semidirect |
| 449. C3 | #71522 | semidirect |
| 450. 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 |
| C3×#5195 | 2 |
| #10590854 | 2 |
| #10590636 | 2 |
| #10589432 | 2 |
| #10589124 | 2 |
| #10589109 | 2 |
| #72113 | 3 |
| #71522 | 3 |