Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
423 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 423 conjugacy classes of subgroups — too many to draw. Only its 90 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. C9×#3676 | C2 | semidirect |
| 5. C23×C92 | C4 | semidirect |
| 8. C2×C4×C92 | C4 | semidirect |
| 24. #63393 | C9 | direct (N × H) |
| 51. #3676 | C2×C9 | semidirect |
| 74. C92 | #99 | semidirect |
| 86. C23×C9 | Dic9 | semidirect |
| 87. C23×C9 | C4×C9 | semidirect |
| 99. C2×C4×C9 | Dic9 | semidirect |
| 100. C2×C4×C9 | C4×C9 | semidirect |
| 226. C9 | #63393 | direct (N × H) |
| 227. C9 | C9×#99 | semidirect |
| 228. C23 | C9×Dic9 | semidirect |
| 232. C2×C4 | C9×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C92 | 2 |
| C9×#3676 | 2 |
| C9×#834 | 3 |
| C3×#63393 | 3 |