Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 498 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. C4×#3697 | C2 | semidirect |
| 3. #10588686 | C2 | semidirect |
| 4. #10588685 | C2 | semidirect |
| 5. C2×#63364 | C2 | semidirect |
| 6. C9×#339 | C2 | semidirect |
| 7. #10588232 | C2 | semidirect |
| 18. #63471 | C4 | semidirect |
| 20. #63470 | C4 | semidirect |
| 49. C2×D36 | C2×C4 | semidirect |
| 54. C2×Dic18 | C2×C4 | semidirect |
| 57. C9×M16 | C2×C4 | semidirect |
| 141. #339 | D9 | semidirect |
| 289. M16 | C4×D9 | semidirect |
| 322. C9 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589850 | 2 |
| C4×#3697 | 2 |
| #10588686 | 2 |
| #10588685 | 2 |
| C2×#63364 | 2 |
| C9×#339 | 2 |
| #10588232 | 2 |
| #68778 | 3 |