Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
606 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 182 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. #10589672 | C2 | semidirect |
| 3. #10588753 | C2 | semidirect |
| 4. #10588752 | C2 | semidirect |
| 5. Q8×C9⋊C8 | C2 | semidirect |
| 6. #10588695 | C2 | semidirect |
| 7. C4×#3672 | C2 | semidirect |
| 70. Q8×C9 | SD16 | semidirect |
| 85. C9⋊C8 | #41 | semidirect |
| 192. C9 | #3392 | semidirect |
| 196. Q8 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#550 | 2 |
| #10589672 | 2 |
| #10588753 | 2 |
| #10588752 | 2 |
| Q8×C9⋊C8 | 2 |
| #10588695 | 2 |
| C4×#3672 | 2 |
| #83588 | 3 |