Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×#63386 | C2 | semidirect |
| 3. #10588821 | C2 | semidirect |
| 4. #10588820 | C2 | semidirect |
| 5. #10588240 | C2 | semidirect |
| 6. #10588174 | C2 | semidirect |
| 7. #10588170 | C2 | semidirect |
| 181. C9 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#472 | 2 |
| C2×#63386 | 2 |
| #10588821 | 2 |
| #10588820 | 2 |
| #10588240 | 2 |
| #10588174 | 2 |
| #10588170 | 2 |
| #71093 | 3 |