Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10588821 | C2 | semidirect |
| 3. #10588589 | C2 | semidirect |
| 4. C2×#63359 | C2 | semidirect |
| 5. C9×#350 | C2 | semidirect |
| 6. #10588193 | C2 | semidirect |
| 7. #10588187 | C2 | semidirect |
| 18. C2×Dic36 | C22 | semidirect |
| 19. C9×M32 | C22 | semidirect |
| 20. C2×C9×C16 | C22 | semidirect |
| 22. #63372 | C22 | semidirect |
| 107. #350 | D9 | semidirect |
| 159. M32 | C2×D9 | semidirect |
| 160. C2×C16 | C2×D9 | semidirect |
| 229. C9 | #2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589854 | 2 |
| #10588821 | 2 |
| #10588589 | 2 |
| C2×#63359 | 2 |
| C9×#350 | 2 |
| #10588193 | 2 |
| #10588187 | 2 |
| #69128 | 3 |