Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 16. #19153023 | C4 | semidirect |
| 17. C8×Dic179 | C4 | semidirect |
| 78. C179 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153048 | 2 |
| #26038475 | 2 |
| #26038397 | 2 |
| #26038210 | 2 |
| #26038196 | 2 |
| #26038195 | 2 |
| #344×C179 | 2 |
| #1833 | 179 |