Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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×D173⋊M16 | C2 | semidirect |
| 2. C2×#19149758 | C2 | semidirect |
| 3. #26012490 | C2 | direct (N × H) |
| 4. C2×#19149744 | C2 | semidirect |
| 6. C2×#14583836 | C22 | semidirect |
| 8. D173⋊M16 | C22 | semidirect |
| 12. #19149758 | C22 | semidirect |
| 15. C2×C4×#10621924 | C22 | semidirect |
| 16. #19149744 | C22 | semidirect |
| 21. C2×#14583827 | C4 | semidirect |
| 22. C2×#14583827 | C4 | semidirect |
| 26. C22×D692 | C4 | semidirect |
| 29. C22×Q8×C173 | C4 | semidirect |
| 32. #14583836 | C23 | semidirect |
| 39. C4×#10621924 | C23 | semidirect |
| 50. #14583827 | C2×C4 | semidirect |
| 59. C2×D692 | C2×C4 | semidirect |
| 76. C2×Q8×C173 | C2×C4 | semidirect |
| 145. C2×C173 | #421 | semidirect |
| 151. C173 | C2×#421 | semidirect |
| 166. C22×Q8 | #10621924 | semidirect |
| 197. C2×Q8 | C2×#10621924 | semidirect |
| 301. C2 | #26012490 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊M16 | 2 |
| C2×#19149758 | 2 |
| #26012490 | 2 |
| C2×#19149744 | 2 |
| C22×#14583827 | 2 |
| C2×#421 | 173 |