Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 3. #10588365 | C2 | semidirect |
| 4. C9×C4⋊C16 | C2 | semidirect |
| 5. #10588180 | C2 | semidirect |
| 66. C4⋊C16 | D9 | semidirect |
| 89. C4×C9 | SD32 | semidirect |
| 148. C9 | #2208 | semidirect |
| 174. C4 | #63359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63359 | 2 |
| C4×D72 | 2 |
| #10588365 | 2 |
| C9×C4⋊C16 | 2 |
| #10588180 | 2 |
| #69287 | 3 |