Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
565 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10589525 | C2 | direct (N × H) |
| 3. C2×#63422 | C2 | semidirect |
| 5. C2×#41⋊C9 | C4 | semidirect |
| 6. C2×#41⋊C9 | C4 | semidirect |
| 9. C22×Q8⋊C9 | C4 | semidirect |
| 11. #63422 | C22 | semidirect |
| 21. #41⋊C9 | C2×C4 | semidirect |
| 24. C2×Q8⋊C9 | C2×C4 | semidirect |
| 309. C2 | #10589525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41⋊C9 | 2 |
| #10589525 | 2 |
| C2×#63422 | 2 |
| C2×#5236 | 3 |
| C2×#3667 | 4 |