Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
286 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 52 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. D173⋊#99 | C2 | semidirect |
| 2. #26012398 | C2 | semidirect |
| 3. #26012395 | C2 | semidirect |
| 8. C2×#14583825 | C4 | semidirect |
| 12. #19149666 | C4 | semidirect |
| 15. #19149636 | C4 | semidirect |
| 16. #127×C173 | C4 | semidirect |
| 22. C2×Dic346 | C2×C4 | semidirect |
| 34. C4×Dic173 | C2×C4 | semidirect |
| 37. C2×D4×C173 | C2×C4 | semidirect |
| 38. C42×C173 | C2×C4 | semidirect |
| 86. C173 | #2127 | semidirect |
| 95. #127 | #10621924 | semidirect |
| 114. C2×D4 | C2×#10621924 | semidirect |
| 125. C42 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#99 | 2 |
| #26012398 | 2 |
| #26012395 | 2 |
| #26012054 | 2 |
| #2127 | 173 |