Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #10588677 | C2 | semidirect |
| 5. C2×C4×C9⋊C8 | C2 | semidirect |
| 6. C9×#339 | C2 | semidirect |
| 7. #10588231 | C2 | semidirect |
| 17. #63369 | C4 | semidirect |
| 18. #63368 | C4 | semidirect |
| 100. #339 | D9 | semidirect |
| 223. C9 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588811 | 2 |
| #10588683 | 2 |
| #10588677 | 2 |
| C2×#63364 | 2 |
| C2×C4×C9⋊C8 | 2 |
| C9×#339 | 2 |
| #10588231 | 2 |
| #68745 | 3 |