Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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. C2×#19149738 | C2 | semidirect |
| 2. #26012398 | C2 | semidirect |
| 3. #26012396 | C2 | semidirect |
| 8. C2×#14583826 | C4 | semidirect |
| 10. #19149676 | C4 | semidirect |
| 12. #19149667 | C4 | semidirect |
| 16. #117×C173 | C4 | semidirect |
| 22. C2×Dic346 | C2×C4 | semidirect |
| 27. C2×D692 | C2×C4 | semidirect |
| 37. C42×C173 | C2×C4 | semidirect |
| 38. C42×C173 | C2×C4 | semidirect |
| 86. C173 | #2127 | semidirect |
| 100. #117 | #10621924 | semidirect |
| 124. C42 | 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 |
|---|---|
| C2×#19149738 | 2 |
| #26012398 | 2 |
| #26012396 | 2 |
| #26012060 | 2 |
| #2127 | 173 |