Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 76 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. #21419370 | C3 | semidirect |
| 3. #21419245 | C3 | semidirect |
| 4. #21419242 | C3 | semidirect |
| 5. #21419232 | C3 | semidirect |
| 6. C32×C27×C31 | C3 | semidirect |
| 54. C32×C27 | C31⋊C3 | semidirect |
| 78. C31 | #10624724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419391 | 3 |
| #21419370 | 3 |
| #21419245 | 3 |
| #21419242 | 3 |
| #21419232 | 3 |
| C32×C27×C31 | 3 |
| #10624724 | 31 |