Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
399 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 86 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. C9×#413 | C2 | semidirect |
| 3. C2×#63396 | C2 | semidirect |
| 4. C2×#63384 | C2 | semidirect |
| 5. #10588814 | C2 | semidirect |
| 6. #10588802 | C2 | semidirect |
| 7. C9⋊#338 | C2 | semidirect |
| 135. #413 | D9 | semidirect |
| 304. C9 | #2050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589925 | 2 |
| C9×#413 | 2 |
| C2×#63396 | 2 |
| C2×#63384 | 2 |
| #10588814 | 2 |
| #10588802 | 2 |
| C9⋊#338 | 2 |
| #70144 | 3 |