Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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. #26012454 | C2 | semidirect |
| 4. #26012373 | C2 | semidirect |
| 8. #19149740 | C4 | semidirect |
| 9. #19149739 | C4 | semidirect |
| 17. C2×#14583809 | C4 | semidirect |
| 19. C22×#13063436 | C4 | semidirect |
| 20. C2×C8×D173 | C4 | semidirect |
| 22. C2×M16×C173 | C4 | semidirect |
| 93. C173 | #1757 | semidirect |
| 106. C2×M16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012477 | 2 |
| #26012470 | 2 |
| #26012454 | 2 |
| #26012373 | 2 |
| C2×#19149687 | 2 |
| #1757 | 173 |