Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
714 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 78 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×#63768 | C2 | semidirect |
| 5. C2×#63767 | C2 | semidirect |
| 11. C2×C32×D8 | C4 | semidirect |
| 12. C2×#3753 | C4 | semidirect |
| 15. C2×#3745 | C4 | semidirect |
| 79. C32×C8 | C22⋊C4 | semidirect |
| 80. C3⋊(C3⋊C8) | C22⋊C4 | semidirect |
| 124. C2×D8 | #157 | semidirect |
| 201. C32 | #1972 | semidirect |
| 227. 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×#63768 | 2 |
| C2×#63767 | 2 |
| #1972 | 9 |