Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
594 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 142 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. C4×C9×M16 | C2 | semidirect |
| 3. C2×#63383 | C2 | semidirect |
| 4. #10588604 | C2 | semidirect |
| 33. C9×M16 | D4 | semidirect |
| 74. C4×M16 | D9 | semidirect |
| 100. C4×C9 | #100 | semidirect |
| 150. M16 | D36 | semidirect |
| 167. C9 | #1965 | semidirect |
| 197. C4 | #63383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63436 | 2 |
| C4×C9×M16 | 2 |
| C2×#63383 | 2 |
| #10588604 | 2 |
| #69876 | 3 |