Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
657 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 146 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. #10589818 | C2 | semidirect |
| 2. #10589818 | C2 | semidirect |
| 3. C9×#493 | C2 | semidirect |
| 4. #10588838 | C2 | semidirect |
| 5. #10588833 | C2 | semidirect |
| 6. #10588753 | C2 | semidirect |
| 7. #10588750 | C2 | semidirect |
| 8. #10588367 | C2 | semidirect |
| 9. #10588361 | C2 | semidirect |
| 134. #493 | D9 | semidirect |
| 302. C9 | #3207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589818 | 2 |
| C9×#493 | 2 |
| #10588838 | 2 |
| #10588833 | 2 |
| #10588753 | 2 |
| #10588750 | 2 |
| #10588367 | 2 |
| #10588361 | 2 |
| #81786 | 3 |