Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
397 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 397 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. #10590250 | C2 | semidirect |
| 4. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 6. C3×#4456 | C2 | semidirect |
| 7. #10589098 | C2 | semidirect |
| 36. #4456 | D3 | semidirect |
| 56. #3715 | C8 | semidirect |
| 104. C3×Dic6 | C2×C8 | semidirect |
| 108. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 109. C3⋊(C3⋊C8) | SD16 | semidirect |
| 216. Dic6 | D3×C8 | semidirect |
| 288. C32 | C8×SD16 | semidirect |
| 333. C3 | #68149 | semidirect |
| 334. C3 | #68212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3715 | 2 |
| #10590329 | 2 |
| #10590250 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C3×#4459 | 2 |
| C3×#4456 | 2 |
| #10589098 | 2 |
| #68212 | 3 |
| #68149 | 3 |