Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
202 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 202 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 |
|---|---|---|
| 123. C31 | #10624588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419306 | 3 |
| 3−1+2×C31⋊C9 | 3 |
| #21419293 | 3 |
| #21419216 | 3 |
| #21419215 | 3 |
| #21419213 | 3 |
| #21419212 | 3 |
| #21419208 | 3 |
| #21419206 | 3 |
| C31×#6858 | 3 |
| #10624588 | 31 |