Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
912 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 246 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×#63455 | C2 | semidirect |
| 3. C2×C9×#106 | C2 | semidirect |
| 4. C2×#63375 | C2 | semidirect |
| 5. C2×#63369 | C2 | semidirect |
| 6. #10588549 | C2 | direct (N × H) |
| 15. C2×D72 | C4 | semidirect |
| 18. #63455 | C22 | semidirect |
| 19. C9×#106 | C22 | semidirect |
| 20. #63375 | C22 | semidirect |
| 21. #63369 | C22 | semidirect |
| 34. C2×D36 | C2×C4 | semidirect |
| 38. C2×C8×C9 | C2×C4 | semidirect |
| 47. D72 | C2×C4 | semidirect |
| 78. D36 | C22×C4 | semidirect |
| 80. C8×C9 | C22×C4 | semidirect |
| 85. C2×#106 | D9 | semidirect |
| 131. #106 | C2×D9 | semidirect |
| 153. C2×C9 | #442 | semidirect |
| 170. C2×C8 | C4×D9 | semidirect |
| 189. C9 | C2×#442 | semidirect |
| 208. C8 | C2×C4×D9 | semidirect |
| 227. C2 | #10588549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D72 | 2 |
| C2×#63455 | 2 |
| C2×C9×#106 | 2 |
| C2×#63375 | 2 |
| C2×#63369 | 2 |
| #10588549 | 2 |
| C2×#4869 | 3 |