Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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×C9×M16 | C2 | semidirect |
| 4. C42×Dic9 | C2 | semidirect |
| 5. #10588235 | C2 | semidirect |
| 14. C4×D36 | C4 | semidirect |
| 17. C4×Dic18 | C4 | semidirect |
| 20. #63384 | C4 | direct (N × H) |
| 37. C9×M16 | C2×C4 | semidirect |
| 50. C4×Dic9 | C2×C4 | semidirect |
| 81. D36 | C42 | semidirect |
| 85. Dic18 | C42 | semidirect |
| 89. C4×M16 | D9 | semidirect |
| 123. C4×C9 | #104 | semidirect |
| 180. M16 | C4×D9 | semidirect |
| 207. C9 | C4×#104 | semidirect |
| 242. C4 | #63384 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3697 | 2 |
| C4×C9×M16 | 2 |
| C2×#63384 | 2 |
| C42×Dic9 | 2 |
| #10588235 | 2 |
| C4×#825 | 3 |