Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 2. #26011515 | C2 | semidirect |
| 3. #26011223 | C2 | semidirect |
| 4. #26011220 | C2 | semidirect |
| 5. #431×C173 | C2 | semidirect |
| 93. C173 | #1495 | semidirect |
| 96. #431 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| #26011515 | 2 |
| #26011223 | 2 |
| #26011220 | 2 |
| #431×C173 | 2 |
| #1495 | 173 |