Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10589847 | C2 | semidirect |
| 3. C9×#421 | C2 | semidirect |
| 4. #10588914 | C2 | semidirect |
| 5. #10588686 | C2 | semidirect |
| 6. #10588235 | C2 | semidirect |
| 7. #10588208 | C2 | semidirect |
| 13. #63509 | C4 | semidirect |
| 14. #63506 | C4 | semidirect |
| 15. #63502 | C4 | semidirect |
| 17. #63498 | C4 | semidirect |
| 55. C9×M16 | D4 | semidirect |
| 70. #3667 | D4 | semidirect |
| 132. #421 | D9 | semidirect |
| 276. M16 | #611 | semidirect |
| 310. C9 | #1884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589934 | 2 |
| #10589847 | 2 |
| C9×#421 | 2 |
| #10588914 | 2 |
| #10588686 | 2 |
| #10588235 | 2 |
| #10588208 | 2 |
| #70417 | 3 |