Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 39. C9×M16 | Q8 | semidirect |
| 57. C4×Dic9 | Q8 | semidirect |
| 59. #3667 | Q8 | semidirect |
| 202. M16 | Dic18 | semidirect |
| 238. C9 | #2061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589621 | 2 |
| C9×#428 | 2 |
| #10588657 | 2 |
| #10588644 | 2 |
| #10588235 | 2 |
| #10588234 | 2 |
| #10588208 | 2 |
| #70667 | 3 |