Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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. #26012560 | C2 | semidirect |
| 2. #26012559 | C2 | semidirect |
| 3. #41×#10621924 | C2 | semidirect |
| 4. C2×Q8×#10621924 | C2 | semidirect |
| 14. #19149727 | C4 | semidirect |
| 15. #19149726 | C4 | semidirect |
| 18. 2−1+4×C173 | C4 | semidirect |
| 26. #14583827 | C2×C4 | semidirect |
| 27. #14583826 | C2×C4 | semidirect |
| 28. #14583825 | C2×C4 | semidirect |
| 29. C2×Dic346 | C2×C4 | semidirect |
| 30. Q8×D173 | C2×C4 | semidirect |
| 34. #41×C173 | C2×C4 | semidirect |
| 35. C2×Q8×C173 | C2×C4 | semidirect |
| 58. #10621924 | 2−1+4 | direct (N × H) |
| 66. C173 | C4×2−1+4 | semidirect |
| 75. 2−1+4 | #10621924 | direct (N × H) |
| 89. #41 | C2×#10621924 | semidirect |
| 93. C2×Q8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012560 | 2 |
| #26012559 | 2 |
| #41×#10621924 | 2 |
| C2×Q8×#10621924 | 2 |
| 2−1+4×D173 | 2 |
| C4×2−1+4 | 173 |