Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
399 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C2×D8×D9 | C2 | semidirect |
| 2. C2×C9×D16 | C2 | semidirect |
| 3. #10588837 | C2 | semidirect |
| 4. C2×#63385 | C2 | semidirect |
| 5. #10588239 | C2 | semidirect |
| 6. #10588186 | C2 | semidirect |
| 7. (C2×D9)⋊C16 | C2 | semidirect |
| 11. C2×C9×D8 | C22 | semidirect |
| 19. C2×C9×C16 | C22 | semidirect |
| 22. #63378 | C22 | semidirect |
| 23. C2×C9⋊C16 | C22 | semidirect |
| 43. C9×D8 | D4 | semidirect |
| 50. D72 | D4 | semidirect |
| 96. C2×D16 | D9 | semidirect |
| 138. C2×D9 | D16 | semidirect |
| 149. C2×D8 | C2×D9 | semidirect |
| 155. C2×C16 | C2×D9 | semidirect |
| 203. D8 | #611 | semidirect |
| 230. C9 | #2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D9 | 2 |
| C2×C9×D16 | 2 |
| #10588837 | 2 |
| C2×#63385 | 2 |
| #10588239 | 2 |
| #10588186 | 2 |
| (C2×D9)⋊C16 | 2 |
| #71467 | 3 |