Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C32×#135 | C2 | semidirect |
| 2. C2×#63655 | C2 | semidirect |
| 3. C2×#63653 | C2 | semidirect |
| 4. #10592814 | C2 | semidirect |
| 5. #10589430 | C2 | semidirect |
| 6. #10589428 | C2 | semidirect |
| 7. #10589415 | C2 | semidirect |
| 24. C2×C3×#135 | D3 | semidirect |
| 41. C32×Q16 | D4 | semidirect |
| 44. C32×D8 | D4 | semidirect |
| 92. C2×#135 | C3⋊D3 | semidirect |
| 109. C3×Q16 | #67 | semidirect |
| 112. C3×D8 | #67 | semidirect |
| 190. Q16 | #638 | semidirect |
| 195. D8 | #638 | semidirect |
| 219. C32 | #2186 | semidirect |
| 262. C3 | #72082 | 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×#63655 | 2 |
| C2×#63653 | 2 |
| #10592814 | 2 |
| #10589430 | 2 |
| #10589428 | 2 |
| #10589415 | 2 |
| #72082 | 3 |