Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
696 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 257 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. C2×#63645 | C2 | semidirect |
| 3. C2×#63639 | C2 | semidirect |
| 4. #10589430 | C2 | semidirect |
| 5. #10589428 | C2 | semidirect |
| 9. C32×#135 | C4 | semidirect |
| 33. C32×Q16 | C2×C4 | semidirect |
| 36. C32×D8 | C2×C4 | semidirect |
| 47. C3×#135 | Dic3 | semidirect |
| 89. C3×Q16 | C2×Dic3 | semidirect |
| 92. C3×D8 | C2×Dic3 | semidirect |
| 114. #135 | C3⋊Dic3 | semidirect |
| 156. Q16 | C2×C3⋊Dic3 | semidirect |
| 159. D8 | C2×C3⋊Dic3 | semidirect |
| 179. C32 | #2139 | semidirect |
| 215. C3 | #72078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#135 | 2 |
| C2×#63645 | 2 |
| C2×#63639 | 2 |
| #10589430 | 2 |
| #10589428 | 2 |
| #72078 | 3 |