Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26012041 | C2 | semidirect |
| 2. #26011804 | C2 | semidirect |
| 3. #26011771 | C2 | semidirect |
| 4. #26011686 | C2 | semidirect |
| 5. #26011625 | C2 | semidirect |
| 6. C4×#14583811 | C2 | semidirect |
| 7. #26011544 | C2 | semidirect |
| 8. C2×C4×D4×C173 | C2 | semidirect |
| 11. #19149679 | C22 | semidirect |
| 12. #19149676 | C22 | semidirect |
| 17. C4×D692 | C22 | semidirect |
| 18. #19149612 | C22 | semidirect |
| 19. C4⋊#13063436 | C22 | semidirect |
| 21. #19149599 | C22 | semidirect |
| 23. C4×#13063436 | C22 | semidirect |
| 81. D4×C173 | #41 | semidirect |
| 88. C2×C4×C173 | D8 | semidirect |
| 120. C173 | #3100 | semidirect |
| 123. C2×C4×D4 | D173 | semidirect |
| 199. D4 | #14583826 | semidirect |
| 208. C2×C4 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011804 | 2 |
| #26011771 | 2 |
| #26011686 | 2 |
| #26011625 | 2 |
| C4×#14583811 | 2 |
| #26011544 | 2 |
| C2×C4×D4×C173 | 2 |
| #3100 | 173 |