Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
236 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 236 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 |
|---|---|---|
| 1. #21419333 | C3 | semidirect |
| 2. #21419314 | C3 | semidirect |
| 3. #21419297 | C3 | semidirect |
| 4. #21419215 | C3 | semidirect |
| 5. #21419214 | C3 | semidirect |
| 6. #21419211 | C3 | semidirect |
| 7. #21419201 | C3 | semidirect |
| 8. #21419200 | C3 | semidirect |
| 9. C31×#6859 | C3 | semidirect |
| 68. #6859 | C31⋊C3 | semidirect |
| 93. C31 | #10624622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419333 | 3 |
| #21419314 | 3 |
| #21419297 | 3 |
| #21419215 | 3 |
| #21419214 | 3 |
| #21419211 | 3 |
| #21419201 | 3 |
| #21419200 | 3 |
| C31×#6859 | 3 |
| #10624622 | 31 |