Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
564 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 141 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. C32×#460 | C2 | semidirect |
| 3. #10592726 | C2 | semidirect |
| 4. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589351 | C2 | semidirect |
| 7. #10589345 | C2 | semidirect |
| 24. C3×#460 | D3 | semidirect |
| 70. C32×Q8 | D8 | semidirect |
| 90. C3⋊(C3⋊C8) | SD16 | semidirect |
| 93. #460 | C3⋊D3 | semidirect |
| 150. C3×Q8 | #213 | semidirect |
| 210. C32 | #1668 | semidirect |
| 214. Q8 | #3753 | semidirect |
| 254. C3 | #71021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#460 | 2 |
| #10592772 | 2 |
| #10592726 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10589410 | 2 |
| #10589351 | 2 |
| #10589345 | 2 |
| #71021 | 3 |