Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26011475 | C2 | semidirect |
| 3. #26011289 | C2 | semidirect |
| 4. #26011287 | C2 | semidirect |
| 5. #413×C173 | C2 | semidirect |
| 111. C173 | #2132 | semidirect |
| 115. #413 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012037 | 2 |
| #26011475 | 2 |
| #26011289 | 2 |
| #26011287 | 2 |
| #413×C173 | 2 |
| #2132 | 173 |