Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
853 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 853 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C24×C9⋊C9 | C2 | semidirect |
| 2. C2×#611⋊C9 | C2 | semidirect |
| 3. #3676⋊C9 | C2 | semidirect |
| 8. C22×D9⋊C9 | C22 | semidirect |
| 10. C2×Dic9⋊C9 | C22 | semidirect |
| 20. C22×C9⋊C9 | D4 | semidirect |
| 26. #63515 | C9 | semidirect |
| 47. C24×C9 | C2×C9 | semidirect |
| 50. C2×#611 | C2×C9 | semidirect |
| 52. #3676 | C2×C9 | semidirect |
| 71. C9⋊C9 | #120 | semidirect |
| 86. C22×D9 | C22×C9 | semidirect |
| 90. C2×Dic9 | C22×C9 | semidirect |
| 127. C22×C9 | D4×C9 | semidirect |
| 161. C24 | D9⋊C9 | semidirect |
| 184. C9 | C9×#120 | semidirect |
| 201. C22 | #611⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C9⋊C9 | 2 |
| C2×#611⋊C9 | 2 |
| #3676⋊C9 | 2 |
| C9×#953 | 3 |
| C3×#63515 | 3 |