Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
387 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. #10590818 | C2 | semidirect |
| 5. #10589139 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 7. #10589104 | C2 | semidirect |
| 17. C3×#827 | C4 | semidirect |
| 49. C3×Dic12 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 73. #827 | Dic3 | semidirect |
| 144. Dic12 | C2×Dic3 | semidirect |
| 148. C3⋊C16 | C2×Dic3 | semidirect |
| 265. C32 | #2175 | semidirect |
| 305. C3 | #69176 | semidirect |
| 306. C3 | #71474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×C3⋊Dic3 | 2 |
| C2×C3×#827 | 2 |
| #10590818 | 2 |
| C3×#4562 | 2 |
| #10589139 | 2 |
| #10589118 | 2 |
| #10589104 | 2 |
| #71474 | 3 |
| #69176 | 3 |