Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19149614 | C2 | semidirect |
| 3. C2×#19149606 | C2 | semidirect |
| 4. C2×#19149605 | C2 | semidirect |
| 5. #26011457 | C2 | semidirect |
| 6. C2×#19149589 | C2 | semidirect |
| 7. #408×C173 | C2 | semidirect |
| 11. C2×#14583816 | C4 | semidirect |
| 12. C2×#14583814 | C4 | semidirect |
| 13. C2×#14583813 | C4 | semidirect |
| 14. C2×#14583811 | C4 | semidirect |
| 119. C173 | #1975 | semidirect |
| 126. #408 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149699 | 2 |
| C2×#19149614 | 2 |
| C2×#19149606 | 2 |
| C2×#19149605 | 2 |
| #26011457 | 2 |
| C2×#19149589 | 2 |
| #408×C173 | 2 |
| #1975 | 173 |