Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. C22×#15668249 | C2 | semidirect |
| 4. C2×#19153036 | C2 | semidirect |
| 6. #26038194 | C2 | semidirect |
| 7. #391×C179 | C2 | semidirect |
| 125. C179 | #2015 | semidirect |
| 132. #391 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668249 | 2 |
| C22×#15668246 | 2 |
| C2×#19153101 | 2 |
| C2×#19153036 | 2 |
| C2×#19153033 | 2 |
| #26038194 | 2 |
| #391×C179 | 2 |
| #2015 | 179 |