Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
213 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10588362 | C2 | semidirect |
| 3. C9×C4⋊C16 | C2 | semidirect |
| 5. #10588181 | C2 | semidirect |
| 32. D72 | Q8 | semidirect |
| 60. C4⋊C16 | D9 | semidirect |
| 134. C9 | #2224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D72 | 2 |
| #10588362 | 2 |
| C9×C4⋊C16 | 2 |
| #10588186 | 2 |
| #10588181 | 2 |
| #69289 | 3 |