Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
204 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 58 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. #21419329 | C3 | semidirect |
| 2. #21419296 | C3 | semidirect |
| 3. C31⋊#6862 | C3 | semidirect |
| 4. #21419214 | C3 | semidirect |
| 6. #21419208 | C3 | semidirect |
| 7. #21419207 | C3 | semidirect |
| 94. C31 | #10624606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419329 | 3 |
| #21419296 | 3 |
| C31⋊#6862 | 3 |
| #21419214 | 3 |
| #21419209 | 3 |
| #21419208 | 3 |
| #21419207 | 3 |
| #21419203 | 3 |
| C9×H(3,𝔽3)×C31 | 3 |
| #10624606 | 31 |