Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2952 conjugacy classes of subgroups; only the 814 normal subgroups are shown.
This group has 2952 conjugacy classes of subgroups — too many to draw. Only its 814 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. C24×Dic9 | C2 | semidirect |
| 3. C22×C9×C22⋊C4 | C2 | semidirect |
| 4. C22×(C2×D9)⋊C4 | C2 | semidirect |
| 5. C22×C4⋊Dic9 | C2 | semidirect |
| 6. C2×#63448 | C2 | direct (N × H) |
| 16. C23×Dic9 | C22 | semidirect |
| 17. C2×C9×C22⋊C4 | C22 | semidirect |
| 18. C2×(C2×D9)⋊C4 | C22 | semidirect |
| 19. C2×C4⋊Dic9 | C22 | semidirect |
| 20. #63448 | C22 | direct (N × H) |
| 43. C22×Dic9 | C23 | semidirect |
| 44. C9×C22⋊C4 | C23 | semidirect |
| 45. (C2×D9)⋊C4 | C23 | semidirect |
| 46. C4⋊Dic9 | C23 | semidirect |
| 85. C22×C22⋊C4 | D9 | semidirect |
| 108. C22×C9 | #123 | semidirect |
| 131. C2×C22⋊C4 | C2×D9 | semidirect |
| 152. C2×C9 | C2×#123 | semidirect |
| 175. C22⋊C4 | C22×D9 | semidirect |
| 189. C9 | C22×#123 | semidirect |
| 219. C22 | #63448 | direct (N × H) |
| 230. C2 | C2×#63448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#611 | 2 |
| C24×Dic9 | 2 |
| C22×C9×C22⋊C4 | 2 |
| C22×(C2×D9)⋊C4 | 2 |
| C22×C4⋊Dic9 | 2 |
| C2×#63448 | 2 |
| C22×#886 | 3 |