Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
222 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×D144 | C2 | semidirect |
| 2. #10588581 | C2 | semidirect |
| 3. #10588577 | C2 | semidirect |
| 4. C9×#368 | C2 | semidirect |
| 5. #10588172 | C2 | semidirect |
| 64. #368 | 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 |
|---|---|
| C2×D144 | 2 |
| #10588581 | 2 |
| #10588577 | 2 |
| C9×#368 | 2 |
| #10588172 | 2 |
| #69361 | 3 |