Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 80 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×#63387 | C2 | semidirect |
| 4. #10588168 | C2 | semidirect |
| 5. C4⋊(C9⋊C16) | C2 | semidirect |
| 27. C9×Q16 | D4 | semidirect |
| 66. C4×Q16 | D9 | semidirect |
| 92. C4×C9 | SD32 | semidirect |
| 129. Q16 | D36 | semidirect |
| 150. C9 | #2207 | semidirect |
| 177. C4 | #63387 | 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×#63387 | 2 |
| #10588377 | 2 |
| #10588168 | 2 |
| C4⋊(C9⋊C16) | 2 |
| #70914 | 3 |