Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
929 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 929 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. #10590312 | C2 | direct (N × H) |
| 29. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 63. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 136. C2×C32 | #500 | semidirect |
| 171. C32 | C2×#500 | semidirect |
| 188. C2×C3 | #5078 | semidirect |
| 202. C3 | C2×#5078 | semidirect |
| 203. C2 | #10590312 | 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 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C2×#63576 | 2 |
| #10590312 | 2 |
| C2×#5078 | 3 |