Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
497 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 497 conjugacy classes of subgroups — too many to draw. Only its 92 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×C16×C3⋊D3 | C2 | semidirect |
| 3. #10590913 | C2 | semidirect |
| 4. C3×#4510 | C2 | semidirect |
| 5. #10589120 | C2 | semidirect |
| 17. C2×C32×C16 | C22 | semidirect |
| 18. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 21. C3×#819 | C22 | semidirect |
| 29. #4510 | D3 | semidirect |
| 72. C2×C3×C16 | C2×D3 | semidirect |
| 75. #819 | C2×D3 | semidirect |
| 175. C2×C16 | D32 | semidirect |
| 221. C3⋊D3 | #359 | semidirect |
| 270. C32 | C2×#359 | semidirect |
| 315. C3 | D3×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594684 | 2 |
| C2×C16×C3⋊D3 | 2 |
| #10590913 | 2 |
| C3×#4510 | 2 |
| #10589120 | 2 |
| D3×#359 | 3 |