Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
735 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 735 conjugacy classes of subgroups — too many to draw. Only its 166 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. C22×#3672 | C2 | semidirect |
| 3. C2×#63471 | C2 | semidirect |
| 4. #10589618 | C2 | semidirect |
| 5. C9×#418 | C2 | semidirect |
| 6. #10588803 | C2 | semidirect |
| 7. #10588683 | C2 | semidirect |
| 8. #10588447 | C2 | semidirect |
| 9. #10588442 | C2 | semidirect |
| 25. C2×#3664 | C22 | semidirect |
| 26. C2×Dic36 | C22 | semidirect |
| 27. #63449 | C22 | semidirect |
| 31. Dic9⋊C8 | C22 | semidirect |
| 32. #63369 | C22 | semidirect |
| 33. #63368 | C22 | semidirect |
| 58. C2×Dic18 | D4 | semidirect |
| 137. #418 | D9 | semidirect |
| 294. C9 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589907 | 2 |
| C22×#3672 | 2 |
| C2×#63471 | 2 |
| #10589618 | 2 |
| C9×#418 | 2 |
| #10588803 | 2 |
| #10588683 | 2 |
| #10588447 | 2 |
| #10588442 | 2 |
| #78945 | 3 |