Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
222 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 68 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×#504 | C2 | semidirect |
| 2. #10588823 | C2 | semidirect |
| 3. C2×D144 | C2 | semidirect |
| 4. #10588193 | C2 | semidirect |
| 5. #10588183 | C2 | semidirect |
| 62. #504 | D9 | semidirect |
| 135. C9 | #2221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#504 | 2 |
| #10588823 | 2 |
| C2×D144 | 2 |
| #10588193 | 2 |
| #10588183 | 2 |
| #71454 | 3 |