Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #26038192 | C2 | semidirect |
| 4. #26038188 | C2 | semidirect |
| 5. #500×C179 | C2 | semidirect |
| 60. C179 | #1675 | semidirect |
| 62. #500 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038726 | 2 |
| C8×D716 | 2 |
| #26038192 | 2 |
| #26038188 | 2 |
| #500×C179 | 2 |
| #1675 | 179 |