Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1386 conjugacy classes of subgroups; only the 394 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 394 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. C2×D4×Dic9 | C2 | semidirect |
| 3. #10588901 | C2 | semidirect |
| 4. #10588615 | C2 | semidirect |
| 5. C42×Dic9 | C2 | semidirect |
| 9. C9×#127 | C4 | semidirect |
| 24. C2×D4×C9 | C2×C4 | semidirect |
| 30. C42×C9 | C2×C4 | semidirect |
| 34. C4×Dic9 | D4 | semidirect |
| 83. C4×C9 | C4×D4 | semidirect |
| 86. Dic9 | #127 | direct (N × H) |
| 89. #127 | Dic9 | direct (N × H) |
| 116. C2×D4 | C2×Dic9 | semidirect |
| 126. C42 | C2×Dic9 | semidirect |
| 137. C9 | C4×#127 | semidirect |
| 164. C4 | D4×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#127 | 2 |
| C2×D4×Dic9 | 2 |
| #10588901 | 2 |
| #10588615 | 2 |
| C42×Dic9 | 2 |
| Dic3×#127 | 3 |