Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
847 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 847 conjugacy classes of subgroups — too many to draw. Only its 148 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. C3×#5819 | C2 | semidirect |
| 3. C3×#5237 | C2 | semidirect |
| 4. C2×#63559 | C2 | semidirect |
| 5. #10589171 | C2 | semidirect |
| 26. #5819 | D3 | semidirect |
| 28. #5237 | D3 | semidirect |
| 54. C3×#208 | D4 | semidirect |
| 184. #208 | #67 | semidirect |
| 348. C32 | #1914 | semidirect |
| 400. C3 | #70137 | semidirect |
| 401. C3 | #72030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596301 | 2 |
| C3×#5819 | 2 |
| C3×#5237 | 2 |
| C2×#63559 | 2 |
| #10589171 | 2 |
| #72030 | 3 |
| #70137 | 3 |