Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
519 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 519 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10589900 | C2 | semidirect |
| 3. C9×#418 | C2 | semidirect |
| 4. #10588819 | C2 | semidirect |
| 5. #10588686 | C2 | semidirect |
| 6. #10588232 | C2 | semidirect |
| 7. #10588210 | C2 | semidirect |
| 18. C2×#3673 | C4 | semidirect |
| 19. C2×#3672 | C4 | semidirect |
| 47. C2×D36 | C2×C4 | semidirect |
| 49. C2×Dic18 | C2×C4 | semidirect |
| 67. C2×C9⋊C8 | C2×C4 | semidirect |
| 120. #418 | D9 | semidirect |
| 284. C9 | #1904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589900 | 2 |
| C2×#63495 | 2 |
| C9×#418 | 2 |
| #10588819 | 2 |
| #10588686 | 2 |
| #10588232 | 2 |
| #10588210 | 2 |
| #70314 | 3 |