Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1854 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 245 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. C32×#407 | C2 | semidirect |
| 3. C4×#3757 | C2 | semidirect |
| 4. C2×#63652 | C2 | semidirect |
| 11. C2×#3828 | C4 | semidirect |
| 13. C22×C4⋊(C3⋊D3) | C4 | semidirect |
| 15. C22×#634 | C4 | semidirect |
| 16. C2×C32×M16 | C22 | semidirect |
| 18. C2×C4×C3⋊Dic3 | C22 | semidirect |
| 24. C3×#407 | D3 | semidirect |
| 71. C2×C3×M16 | C2×D3 | semidirect |
| 107. C4⋊(C3⋊D3) | C22⋊C4 | semidirect |
| 112. #634 | C22⋊C4 | semidirect |
| 116. #407 | C3⋊D3 | semidirect |
| 159. C22×C32 | #104 | semidirect |
| 182. C2×M16 | C2×C3⋊D3 | semidirect |
| 273. C22×C3 | #825 | semidirect |
| 286. C32 | #1789 | semidirect |
| 342. C22 | #63652 | semidirect |
| 351. C3 | #69991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3828 | 2 |
| C32×#407 | 2 |
| C4×#3757 | 2 |
| C2×#63652 | 2 |
| #69991 | 3 |