Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
243 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 88 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. C4×C9×Q16 | C2 | semidirect |
| 4. #10588241 | C2 | semidirect |
| 6. #10588167 | C2 | semidirect |
| 7. C4×C9⋊C16 | C2 | semidirect |
| 16. #63387 | C4 | direct (N × H) |
| 32. C9×Q16 | C2×C4 | semidirect |
| 44. C9⋊C16 | C2×C4 | semidirect |
| 74. C4×Q16 | D9 | semidirect |
| 104. C4×C9 | SD32 | semidirect |
| 143. Q16 | C4×D9 | semidirect |
| 167. C9 | C4×SD32 | semidirect |
| 195. C4 | #63387 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×Q16 | 2 |
| C2×#63387 | 2 |
| C4×D72 | 2 |
| #10588241 | 2 |
| #10588168 | 2 |
| #10588167 | 2 |
| C4×C9⋊C16 | 2 |
| C4×#828 | 3 |