Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 128 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×C4⋊C4 | C2 | semidirect |
| 3. C2×#63364 | C2 | semidirect |
| 4. C4×#3667 | C2 | semidirect |
| 13. #63437 | C4 | semidirect |
| 14. #63436 | C4 | semidirect |
| 17. #63431 | C4 | semidirect |
| 49. #3667 | D4 | semidirect |
| 95. C4×C4⋊C4 | D9 | semidirect |
| 133. C4×C9 | #104 | semidirect |
| 224. C9 | #1980 | semidirect |
| 268. C4 | #63364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589579 | 2 |
| C4×C9×C4⋊C4 | 2 |
| C2×#63364 | 2 |
| C4×#3667 | 2 |
| #69492 | 3 |