Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
984 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 1. C2×C9×#127 | C2 | semidirect |
| 2. C2×#63495 | C2 | semidirect |
| 3. #10589579 | C2 | semidirect |
| 4. #10588756 | C2 | semidirect |
| 5. #10588755 | C2 | semidirect |
| 6. #10588753 | C2 | semidirect |
| 7. C4×#3667 | C2 | semidirect |
| 17. C2×#3673 | C22 | semidirect |
| 18. C2×#3672 | C22 | semidirect |
| 21. #63437 | C22 | semidirect |
| 22. #63436 | C22 | semidirect |
| 24. #63431 | C22 | semidirect |
| 25. #63362 | C22 | semidirect |
| 26. C4×C9⋊C8 | C22 | semidirect |
| 56. #3667 | D4 | semidirect |
| 98. C9⋊C8 | C2×D4 | semidirect |
| 101. C2×#127 | D9 | semidirect |
| 140. C4×C9 | AGL(1,ℤ/8) | semidirect |
| 225. C9 | #3151 | semidirect |
| 263. C4 | #63495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#127 | 2 |
| C2×#63495 | 2 |
| #10589579 | 2 |
| #10588756 | 2 |
| #10588755 | 2 |
| #10588753 | 2 |
| C4×#3667 | 2 |
| #83163 | 3 |