Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19149613 | C2 | semidirect |
| 4. #26011253 | C2 | semidirect |
| 5. C2×#107×C173 | C2 | semidirect |
| 10. C2×C8×D173 | C4 | semidirect |
| 69. C8×C173 | C22⋊C4 | semidirect |
| 83. C2×D173 | #107 | semidirect |
| 99. C173 | #1808 | semidirect |
| 103. C2×#107 | D173 | semidirect |
| 169. C8 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D173 | 2 |
| C2×#19149613 | 2 |
| #26011348 | 2 |
| #26011253 | 2 |
| C2×#107×C173 | 2 |
| #1808 | 173 |