Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
258 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10588552 | C2 | semidirect |
| 3. C9×#367 | C2 | semidirect |
| 4. #10588179 | C2 | semidirect |
| 5. #10588168 | C2 | semidirect |
| 14. D144 | C4 | semidirect |
| 28. D72 | C2×C4 | semidirect |
| 29. C9×C16 | C2×C4 | semidirect |
| 52. #367 | D9 | semidirect |
| 105. C16 | C4×D9 | semidirect |
| 114. C9 | #2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D144 | 2 |
| #10588552 | 2 |
| C9×#367 | 2 |
| #10588179 | 2 |
| #10588168 | 2 |
| #69339 | 3 |