Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3373 conjugacy classes of subgroups; only the 652 normal subgroups are shown.
This group has 3373 conjugacy classes of subgroups — too many to draw. Only its 652 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. C22×#3797 | C2 | semidirect |
| 3. C22×C3×#214 | C2 | semidirect |
| 4. C2×#63931 | C2 | direct (N × H) |
| 5. C22×#3719 | C2 | semidirect |
| 6. C22×#3712 | C2 | semidirect |
| 19. C2×#3797 | C22 | semidirect |
| 20. C2×C3×#214 | C22 | semidirect |
| 22. #63931 | C22 | direct (N × H) |
| 23. C2×#3719 | C22 | semidirect |
| 24. C2×#3712 | C22 | semidirect |
| 30. C22×#214 | D3 | semidirect |
| 55. #3797 | C23 | semidirect |
| 56. C3×#214 | C23 | semidirect |
| 58. #3719 | C23 | semidirect |
| 59. #3712 | C23 | semidirect |
| 84. C2×#214 | C2×D3 | semidirect |
| 161. #214 | C22×D3 | semidirect |
| 167. C22×C32 | #137 | semidirect |
| 238. C2×C32 | C2×#137 | semidirect |
| 273. C22×C3 | #915 | semidirect |
| 289. C32 | C22×#137 | semidirect |
| 317. C2×C3 | C2×#915 | semidirect |
| 325. C22 | #63931 | direct (N × H) |
| 333. C3 | C22×#915 | semidirect |
| 336. C2 | C2×#63931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3830 | 2 |
| C22×#3797 | 2 |
| C22×C3×#214 | 2 |
| C2×#63931 | 2 |
| C22×#3719 | 2 |
| C22×#3712 | 2 |
| C22×#915 | 3 |