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 |
|---|---|---|
| 2. #10592775 | C2 | semidirect |
| 3. D4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10592706 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589352 | C2 | semidirect |
| 7. #10589346 | C2 | semidirect |
| 75. C32×D4 | SD16 | semidirect |
| 89. C3⋊(C3⋊C8) | D8 | semidirect |
| 154. C3×D4 | #214 | semidirect |
| 208. C32 | #1665 | semidirect |
| 219. D4 | #3754 | semidirect |
| 251. C3 | #71004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#459 | 2 |
| #10592775 | 2 |
| D4×C3⋊(C3⋊C8) | 2 |
| #10592706 | 2 |
| #10589410 | 2 |
| #10589352 | 2 |
| #10589346 | 2 |
| #71004 | 3 |