Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1185 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 1185 conjugacy classes of subgroups — too many to draw. Only its 316 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 |
|---|---|---|
| 4. #10590387 | C2 | direct (N × H) |
| 51. C2×C32×C4 | Q16 | semidirect |
| 92. C32×C4 | C2×Q16 | semidirect |
| 115. C2×C3×C4 | #216 | semidirect |
| 126. C2×C32 | #494 | semidirect |
| 152. C3×C4 | C2×#216 | semidirect |
| 155. C32 | C2×#494 | semidirect |
| 161. C2×C4 | #3718 | semidirect |
| 170. C2×C3 | #5092 | semidirect |
| 177. C4 | C2×#3718 | semidirect |
| 181. C3 | C2×#5092 | semidirect |
| 182. C2 | #10590387 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#869 | 2 |
| C22×#3718 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10590387 | 2 |
| C2×#5092 | 3 |