Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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×C4⋊C8 | C2 | semidirect |
| 3. C2×#63380 | C2 | semidirect |
| 4. #10588619 | C2 | semidirect |
| 5. #10588229 | C2 | semidirect |
| 69. C2×C4×C9 | D8 | semidirect |
| 84. C2×C4⋊C8 | D9 | semidirect |
| 211. C9 | #2054 | semidirect |
| 231. C2×C4 | D72 | 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×C4⋊C8 | 2 |
| C2×#63380 | 2 |
| #10588619 | 2 |
| #10588229 | 2 |
| #70481 | 3 |