Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
270 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 90 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. C9×#436 | C2 | semidirect |
| 3. #10588370 | C2 | semidirect |
| 4. D4⋊(C9⋊C8) | C2 | semidirect |
| 5. #10588162 | C2 | semidirect |
| 6. #10588156 | C2 | semidirect |
| 7. C8×C9⋊C8 | C2 | semidirect |
| 83. C8×C9 | D8 | semidirect |
| 87. C9⋊C8 | M16 | semidirect |
| 90. #436 | D9 | semidirect |
| 203. C9 | #1589 | semidirect |
| 225. C8 | #3673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#436 | 2 |
| C4×#3673 | 2 |
| #10588370 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #10588162 | 2 |
| #10588156 | 2 |
| C8×C9⋊C8 | 2 |
| #70859 | 3 |