Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
722 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10593827 | C2 | semidirect |
| 3. C2×#63782 | C2 | semidirect |
| 4. C2×#63769 | C2 | semidirect |
| 5. C2×C8×#157 | C2 | semidirect |
| 11. C2×C32×D8 | C4 | semidirect |
| 12. C2×#3753 | C4 | semidirect |
| 15. C2×#3745 | C4 | semidirect |
| 66. C2×#157 | D8 | semidirect |
| 80. C32×C8 | C22⋊C4 | semidirect |
| 81. C3⋊(C3⋊C8) | C22⋊C4 | semidirect |
| 126. C2×D8 | #157 | semidirect |
| 205. C32 | #1970 | semidirect |
| 232. C8 | C22⋊#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×C3⋊D3 | 2 |
| #10593827 | 2 |
| C2×#63782 | 2 |
| C2×#63769 | 2 |
| C2×C8×#157 | 2 |
| #1970 | 9 |