Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
564 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 146 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×C9×#106 | C2 | semidirect |
| 3. C2×#63375 | C2 | semidirect |
| 4. #10588668 | C2 | semidirect |
| 5. C2×#63369 | C2 | semidirect |
| 15. C2×D72 | C4 | semidirect |
| 79. C8×C9 | C22⋊C4 | semidirect |
| 82. C2×#106 | D9 | semidirect |
| 199. C9 | #1972 | semidirect |
| 221. C8 | (C2×D9)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D72 | 2 |
| C2×C9×#106 | 2 |
| C2×#63375 | 2 |
| #10588668 | 2 |
| C2×#63369 | 2 |
| #70576 | 3 |