Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 3. #10588553 | C2 | semidirect |
| 5. #10588180 | C2 | semidirect |
| 6. #10588179 | C2 | semidirect |
| 7. #10588166 | C2 | semidirect |
| 16. #63386 | C4 | semidirect |
| 42. Dic36 | C2×C4 | semidirect |
| 44. C9⋊C16 | C2×C4 | semidirect |
| 167. C9 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic9 | 2 |
| C2×#63386 | 2 |
| #10588553 | 2 |
| C9×#357 | 2 |
| #10588180 | 2 |
| #10588179 | 2 |
| #10588166 | 2 |
| #69176 | 3 |