Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1653 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 1653 conjugacy classes of subgroups — too many to draw. Only its 262 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. C24×Dic9 | C2 | semidirect |
| 3. C2×#63497 | C2 | semidirect |
| 4. #10588927 | C2 | semidirect |
| 5. #10588900 | C2 | semidirect |
| 6. #10588626 | C2 | semidirect |
| 7. #10588623 | C2 | semidirect |
| 21. C2×#3676 | C22 | semidirect |
| 23. C2×Dic9⋊C4 | C22 | semidirect |
| 24. C9⋊#95 | C22 | semidirect |
| 49. C22×Dic9 | D4 | semidirect |
| 145. C22×C9 | #123 | semidirect |
| 246. C9 | #2849 | semidirect |
| 289. C22 | #63497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic9 | 2 |
| C2×C9×#120 | 2 |
| C2×#63497 | 2 |
| #10588927 | 2 |
| #10588900 | 2 |
| #10588626 | 2 |
| #10588623 | 2 |
| #82602 | 3 |