Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
555 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 110 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. #10589625 | C2 | semidirect |
| 3. C9×#418 | C2 | semidirect |
| 4. #10588901 | C2 | semidirect |
| 5. C2×#63384 | C2 | semidirect |
| 6. #10588234 | C2 | semidirect |
| 7. #10588208 | C2 | semidirect |
| 15. #63495 | C4 | semidirect |
| 42. C2×D4×C9 | C2×C4 | semidirect |
| 73. #3667 | C2×C4 | semidirect |
| 124. D36 | C22⋊C4 | semidirect |
| 129. Dic18 | C22⋊C4 | semidirect |
| 135. #418 | D9 | semidirect |
| 276. C2×D4 | C4×D9 | semidirect |
| 324. C9 | #1883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63495 | 2 |
| #10589625 | 2 |
| C9×#418 | 2 |
| #10588901 | 2 |
| C2×#63384 | 2 |
| #10588234 | 2 |
| #10588208 | 2 |
| #70328 | 3 |