Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
594 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×C9×#100 | C2 | semidirect |
| 3. C2×#63391 | C2 | semidirect |
| 4. C2×#63383 | C2 | semidirect |
| 5. C2×#63383 | C2 | semidirect |
| 6. #10588802 | C2 | semidirect |
| 7. M16×Dic9 | C2 | semidirect |
| 56. C9×M16 | D4 | semidirect |
| 65. #3667 | D4 | semidirect |
| 124. C2×#100 | D9 | semidirect |
| 177. Dic9 | #100 | semidirect |
| 260. M16 | #611 | semidirect |
| 286. C9 | #1965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63502 | 2 |
| C2×C9×#100 | 2 |
| C2×#63391 | 2 |
| C2×#63383 | 2 |
| #10588802 | 2 |
| M16×Dic9 | 2 |
| #70064 | 3 |