Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
226 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 52 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. #21419391 | C3 | semidirect |
| 2. #21419268 | C3 | semidirect |
| 3. #21419265 | C3 | semidirect |
| 4. #21419261 | C3 | semidirect |
| 5. #21419260 | C3 | semidirect |
| 6. C3×C92×C31 | C3 | semidirect |
| 50. C3×C92 | C31⋊C3 | semidirect |
| 71. C31 | #10624837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419391 | 3 |
| #21419268 | 3 |
| #21419265 | 3 |
| #21419261 | 3 |
| #21419260 | 3 |
| C3×C92×C31 | 3 |
| #10624837 | 31 |