Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
188 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 188 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. #21419296 | C3 | semidirect |
| 3. #21419282 | C3 | semidirect |
| 4. #21419279 | C3 | semidirect |
| 5. #21419277 | C3 | semidirect |
| 6. #21419274 | C3 | semidirect |
| 7. #21419272 | C3 | semidirect |
| 8. #21419269 | C3 | semidirect |
| 9. C31×#6908 | C3 | semidirect |
| 64. #6908 | C31⋊C3 | semidirect |
| 95. C31 | #10624845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419391 | 3 |
| #21419296 | 3 |
| #21419282 | 3 |
| #21419279 | 3 |
| #21419277 | 3 |
| #21419274 | 3 |
| #21419272 | 3 |
| #21419269 | 3 |
| C31×#6908 | 3 |
| #10624845 | 31 |