Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1530 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1530 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×#3753 | C2 | semidirect |
| 2. C2×#64083 | C2 | semidirect |
| 3. C32×#390 | C2 | semidirect |
| 4. C2×#63636 | C2 | semidirect |
| 5. #10589390 | C2 | semidirect |
| 21. C3×#390 | D3 | semidirect |
| 29. C2×C32×D4 | D4 | semidirect |
| 48. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 79. C2×C32×C4 | D8 | semidirect |
| 93. #390 | C3⋊D3 | semidirect |
| 100. C2×C3×D4 | D12 | semidirect |
| 168. C2×C3×C4 | #213 | semidirect |
| 200. C2×D4 | C4⋊(C3⋊D3) | semidirect |
| 230. C32 | #2011 | semidirect |
| 253. C2×C4 | #3753 | semidirect |
| 285. C3 | #69658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3753 | 2 |
| C2×#64083 | 2 |
| C32×#390 | 2 |
| C2×#63636 | 2 |
| #10589390 | 2 |
| #69658 | 3 |