Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C16×D9 | C2 | semidirect |
| 3. D9×#108 | C2 | semidirect |
| 4. C9×#359 | C2 | semidirect |
| 5. #10588244 | C2 | semidirect |
| 6. #10588187 | C2 | semidirect |
| 7. #10588173 | C2 | semidirect |
| 21. C2×C9×C16 | C22 | semidirect |
| 22. C9×#108 | C22 | semidirect |
| 24. #63372 | C22 | semidirect |
| 25. C2×C9⋊C16 | C22 | semidirect |
| 123. #359 | D9 | direct (N × H) |
| 185. C2×C16 | C2×D9 | semidirect |
| 188. #108 | C2×D9 | semidirect |
| 223. D9 | #359 | direct (N × H) |
| 270. C9 | C2×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D9×#135 | 2 |
| C2×C16×D9 | 2 |
| D9×#108 | 2 |
| C9×#359 | 2 |
| #10588244 | 2 |
| #10588187 | 2 |
| #10588173 | 2 |
| D3×#359 | 3 |