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×#216 | C2 | semidirect |
| 4. C2×#63945 | C2 | direct (N × H) |
| 5. C22×#3717 | C2 | semidirect |
| 6. C22×#3712 | C2 | semidirect |
| 19. C2×#3797 | C22 | semidirect |
| 20. C2×C3×#216 | C22 | semidirect |
| 22. #63945 | C22 | direct (N × H) |
| 23. C2×#3717 | C22 | semidirect |
| 24. C2×#3712 | C22 | semidirect |
| 29. C22×#216 | D3 | semidirect |
| 55. #3797 | C23 | semidirect |
| 56. C3×#216 | C23 | semidirect |
| 58. #3717 | C23 | semidirect |
| 59. #3712 | C23 | semidirect |
| 83. C2×#216 | C2×D3 | semidirect |
| 160. #216 | C22×D3 | semidirect |
| 165. C22×C32 | #137 | semidirect |
| 237. C2×C32 | C2×#137 | semidirect |
| 269. C22×C3 | #918 | semidirect |
| 289. C32 | C22×#137 | semidirect |
| 315. C2×C3 | C2×#918 | semidirect |
| 325. C22 | #63945 | direct (N × H) |
| 333. C3 | C22×#918 | semidirect |
| 336. C2 | C2×#63945 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3832 | 2 |
| C22×#3797 | 2 |
| C22×C3×#216 | 2 |
| C2×#63945 | 2 |
| C22×#3717 | 2 |
| C22×#3712 | 2 |
| C22×#918 | 3 |