Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10590259 | C2 | semidirect |
| 4. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 6. C3×#4456 | C2 | semidirect |
| 7. #10589098 | C2 | semidirect |
| 36. #4456 | D3 | semidirect |
| 108. C3⋊(C3⋊C8) | M16 | semidirect |
| 109. C3⋊(C3⋊C8) | SD16 | semidirect |
| 288. C32 | #1590 | semidirect |
| 333. C3 | #68161 | semidirect |
| 334. C3 | #68224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3715 | 2 |
| #10590339 | 2 |
| #10590259 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C3×#4459 | 2 |
| C3×#4456 | 2 |
| #10589098 | 2 |
| #68224 | 3 |
| #68161 | 3 |