Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
213 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 213 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 |
|---|---|---|
| 2. #10588560 | C2 | semidirect |
| 3. C9×#357 | C2 | semidirect |
| 4. #10588239 | C2 | semidirect |
| 5. (C2×D9)⋊C16 | C2 | semidirect |
| 6. #10588181 | C2 | semidirect |
| 7. #10588167 | C2 | semidirect |
| 76. #357 | D9 | semidirect |
| 169. C9 | #2234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588837 | 2 |
| #10588560 | 2 |
| C9×#357 | 2 |
| #10588239 | 2 |
| (C2×D9)⋊C16 | 2 |
| #10588181 | 2 |
| #10588167 | 2 |
| #69201 | 3 |