Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
519 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 519 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. #10589623 | C2 | semidirect |
| 3. #10588819 | C2 | semidirect |
| 4. #10588813 | C2 | semidirect |
| 5. #10588686 | C2 | semidirect |
| 6. C9×#344 | C2 | semidirect |
| 7. #10588237 | C2 | semidirect |
| 18. C2×D72 | C4 | semidirect |
| 19. C2×#3664 | C4 | semidirect |
| 44. C2×D36 | C2×C4 | semidirect |
| 49. C2×Dic18 | C2×C4 | semidirect |
| 55. C2×C8×C9 | C2×C4 | semidirect |
| 122. #344 | D9 | semidirect |
| 255. C2×C8 | C4×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 |
|---|---|
| C2×#63470 | 2 |
| #10589623 | 2 |
| #10588819 | 2 |
| #10588813 | 2 |
| #10588686 | 2 |
| C9×#344 | 2 |
| #10588237 | 2 |
| #69027 | 3 |