Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
245 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×#4463 | C2 | semidirect |
| 3. C3×#4455 | C2 | semidirect |
| 5. #67767 | C3 | direct (N × H) |
| 18. #4463 | C2×C3 | semidirect |
| 19. #4455 | C2×C3 | semidirect |
| 21. C32×Q16 | C8 | semidirect |
| 23. C32×D8 | C8 | semidirect |
| 71. C3×Q16 | C3⋊C8 | semidirect |
| 72. C3×Q16 | C3×C8 | semidirect |
| 77. C3×D8 | C3⋊C8 | semidirect |
| 78. C3×D8 | C3×C8 | semidirect |
| 153. Q16 | C3×C3⋊C8 | semidirect |
| 155. D8 | C3×C3⋊C8 | semidirect |
| 182. C32 | #1336 | semidirect |
| 211. C3 | #67767 | direct (N × H) |
| 212. C3 | C3×#1336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#443 | 2 |
| C3×#4463 | 2 |
| C3×#4455 | 2 |
| C3×#1336 | 3 |
| #67767 | 3 |