Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26011361 | C2 | semidirect |
| 4. #26011254 | C2 | semidirect |
| 5. C2×C4⋊C8×C173 | C2 | semidirect |
| 9. C4×D692 | C4 | semidirect |
| 56. D692 | C4⋊C4 | semidirect |
| 93. C4×C173 | #102 | semidirect |
| 108. C173 | #1802 | semidirect |
| 111. C2×C4⋊C8 | D173 | semidirect |
| 204. C4 | #19149601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| C2×#19149601 | 2 |
| #26011361 | 2 |
| #26011254 | 2 |
| C2×C4⋊C8×C173 | 2 |
| #1802 | 173 |