Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 136 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. M16×Dic9 | C2 | semidirect |
| 4. C9×#343 | C2 | semidirect |
| 5. #10588207 | C2 | semidirect |
| 16. #63383 | C4 | semidirect |
| 37. C9×M16 | C2×C4 | semidirect |
| 44. #3667 | C2×C4 | semidirect |
| 86. #343 | D9 | semidirect |
| 124. Dic9 | #100 | semidirect |
| 181. M16 | C4×D9 | semidirect |
| 204. C9 | C4×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63455 | 2 |
| C2×#63383 | 2 |
| M16×Dic9 | 2 |
| C9×#343 | 2 |
| #10588207 | 2 |
| #68972 | 3 |