Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10588875 | C2 | semidirect |
| 3. C2×#63386 | C2 | semidirect |
| 4. #10588821 | C2 | semidirect |
| 5. #10588244 | C2 | semidirect |
| 6. #10588240 | C2 | semidirect |
| 7. #10588238 | C2 | semidirect |
| 18. C2×Dic36 | C22 | semidirect |
| 23. #63372 | C22 | semidirect |
| 24. #63371 | C22 | semidirect |
| 25. C2×C9⋊C16 | C22 | semidirect |
| 229. C9 | #2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#576 | 2 |
| #10588875 | 2 |
| C2×#63386 | 2 |
| #10588821 | 2 |
| #10588244 | 2 |
| #10588240 | 2 |
| #10588238 | 2 |
| #72123 | 3 |