Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 162 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×#19149767 | C2 | semidirect |
| 2. C2×#19149766 | C2 | semidirect |
| 3. #26012536 | C2 | direct (N × H) |
| 4. C2×#19149750 | C2 | semidirect |
| 5. C2×#19149744 | C2 | semidirect |
| 6. C2×#19149743 | C2 | semidirect |
| 7. C2×#19149733 | C2 | semidirect |
| 10. #19149767 | C22 | semidirect |
| 12. #19149766 | C22 | semidirect |
| 21. #19149750 | C22 | semidirect |
| 22. #19149744 | C22 | semidirect |
| 23. #19149743 | C22 | semidirect |
| 24. #19149733 | C22 | semidirect |
| 27. #19149700 | C4 | semidirect |
| 29. C2×#14583816 | C4 | semidirect |
| 30. C2×#14583815 | C4 | semidirect |
| 31. C2×#14583811 | C4 | semidirect |
| 33. C2×SD16×C173 | C4 | semidirect |
| 66. #14583816 | C2×C4 | semidirect |
| 67. #14583815 | C2×C4 | semidirect |
| 68. #14583811 | C2×C4 | semidirect |
| 74. SD16×C173 | C2×C4 | semidirect |
| 127. C2×C173 | #444 | semidirect |
| 132. C173 | C2×#444 | semidirect |
| 148. C2×SD16 | #10621924 | semidirect |
| 187. SD16 | C2×#10621924 | semidirect |
| 263. C2 | #26012536 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| C2×#19149766 | 2 |
| #26012536 | 2 |
| C2×#19149750 | 2 |
| C2×#19149744 | 2 |
| C2×#19149743 | 2 |
| C2×#19149733 | 2 |
| C2×#19149700 | 2 |
| C2×#444 | 173 |