Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
128 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 49 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. #21419253 | C3 | semidirect |
| 3. #21419253 | C3 | semidirect |
| 4. #21419252 | C3 | semidirect |
| 5. #21419252 | C3 | semidirect |
| 6. #21419251 | C3 | semidirect |
| 7. #21419250 | C3 | semidirect |
| 8. #21419249 | C3 | semidirect |
| 9. #21419249 | C3 | semidirect |
| 13. C31×#6875 | C3 | semidirect |
| 70. #6875 | C31⋊C3 | semidirect |
| 93. C31 | #10624830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419295 | 3 |
| #21419253 | 3 |
| #21419252 | 3 |
| #21419251 | 3 |
| #21419250 | 3 |
| #21419249 | 3 |
| #21419231 | 3 |
| C31×#6875 | 3 |
| #10624830 | 31 |