Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
237 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 237 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 |
|---|---|---|
| 1. C4×C9×Q16 | C2 | semidirect |
| 2. C2×#63388 | C2 | semidirect |
| 5. #10588169 | C2 | semidirect |
| 7. C4⋊(C9⋊C16) | C2 | semidirect |
| 82. C4×Q16 | D9 | semidirect |
| 181. C9 | #2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×Q16 | 2 |
| C2×#63388 | 2 |
| C2×#63387 | 2 |
| #10588378 | 2 |
| #10588169 | 2 |
| #10588168 | 2 |
| C4⋊(C9⋊C16) | 2 |
| #70915 | 3 |