Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
770 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 106 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×C4⋊#622 | C2 | semidirect |
| 3. C2×C4×#622 | C2 | semidirect |
| 4. #10590160 | C2 | direct (N × H) |
| 17. C4⋊#622 | C22 | semidirect |
| 19. C4×#622 | C22 | semidirect |
| 28. C2×C4⋊(C3⋊D3) | C8 | semidirect |
| 76. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 163. C2×C32 | D4⋊C8 | semidirect |
| 210. C32 | C2×D4⋊C8 | semidirect |
| 261. C2 | #10590160 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64102 | 2 |
| C2×C4⋊#622 | 2 |
| C2×C4×#622 | 2 |
| #10590160 | 2 |
| C2×D4⋊C8 | 9 |