Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
384 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 3. C2×#63381 | C2 | semidirect |
| 5. #10588676 | C2 | semidirect |
| 6. C9×#344 | C2 | semidirect |
| 7. #10588232 | C2 | semidirect |
| 18. #63469 | C4 | semidirect |
| 19. #63469 | C4 | semidirect |
| 121. #344 | D9 | semidirect |
| 266. C9 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63469 | 2 |
| #10588819 | 2 |
| C2×#63381 | 2 |
| #10588685 | 2 |
| #10588676 | 2 |
| C9×#344 | 2 |
| #10588232 | 2 |
| #69032 | 3 |