Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1422 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 1. C22×#3755 | C2 | semidirect |
| 3. C32×#391 | C2 | semidirect |
| 4. C2×#63636 | C2 | semidirect |
| 5. #10589390 | C2 | semidirect |
| 21. C3×#391 | D3 | semidirect |
| 28. C2×C32×Q8 | D4 | semidirect |
| 47. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 76. C2×C32×C4 | SD16 | semidirect |
| 90. #391 | C3⋊D3 | semidirect |
| 96. C2×C3×Q8 | D12 | semidirect |
| 158. C2×C3×C4 | #215 | semidirect |
| 179. C2×Q8 | C4⋊(C3⋊D3) | semidirect |
| 214. C32 | #2014 | semidirect |
| 235. C2×C4 | #3755 | semidirect |
| 262. C3 | #69688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3755 | 2 |
| C2×#64083 | 2 |
| C32×#391 | 2 |
| C2×#63636 | 2 |
| #10589390 | 2 |
| #69688 | 3 |