Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26012258 | C2 | semidirect |
| 3. C2×#19149595 | C2 | semidirect |
| 4. #26011262 | C2 | semidirect |
| 5. #413×C173 | C2 | semidirect |
| 28. #14583810 | D4 | semidirect |
| 85. C173 | #1914 | semidirect |
| 89. #413 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012258 | 2 |
| #26012055 | 2 |
| C2×#19149595 | 2 |
| #26011262 | 2 |
| #413×C173 | 2 |
| #1914 | 173 |