Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 2. C4×#14583836 | C2 | semidirect |
| 3. C42×#10621924 | C2 | semidirect |
| 4. #26012361 | C2 | semidirect |
| 10. #19149744 | C4 | direct (N × H) |
| 14. Q8×Dic173 | C4 | semidirect |
| 16. C4×D692 | C4 | semidirect |
| 18. #19149641 | C4 | semidirect |
| 23. C4×Q8×C173 | C4 | semidirect |
| 26. #14583836 | C2×C4 | semidirect |
| 31. C4×#10621924 | C2×C4 | semidirect |
| 65. D692 | C42 | semidirect |
| 78. Q8×C173 | C42 | semidirect |
| 95. C4×C173 | #104 | semidirect |
| 100. Dic173 | #104 | semidirect |
| 107. C173 | C4×#104 | semidirect |
| 117. C4×Q8 | #10621924 | semidirect |
| 168. Q8 | C4×#10621924 | semidirect |
| 207. C4 | #19149744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149744 | 2 |
| C4×#14583836 | 2 |
| C42×#10621924 | 2 |
| #26012361 | 2 |
| C4×#14583827 | 2 |
| C4×#104 | 173 |