Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 88 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. C4×D72 | C2 | semidirect |
| 3. C4×C9×C16 | C2 | semidirect |
| 4. #10588186 | C2 | semidirect |
| 5. #10588181 | C2 | semidirect |
| 14. D144 | C4 | direct (N × H) |
| 28. D72 | C2×C4 | semidirect |
| 30. C9×C16 | C2×C4 | semidirect |
| 55. C4×C16 | D9 | semidirect |
| 72. C4×C9 | D16 | semidirect |
| 109. C16 | C4×D9 | semidirect |
| 119. C9 | C4×D16 | semidirect |
| 141. C4 | D144 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D144 | 2 |
| C4×D72 | 2 |
| C4×C9×C16 | 2 |
| #10588186 | 2 |
| #10588181 | 2 |
| C4×D48 | 3 |