Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 13. #19149740 | C4 | semidirect |
| 18. #19149598 | C4 | semidirect |
| 19. #19149597 | C4 | semidirect |
| 20. #101×C173 | C4 | semidirect |
| 74. #10621924 | #101 | direct (N × H) |
| 84. C173 | C4×#101 | semidirect |
| 103. #101 | #10621924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10621924 | 2 |
| D173⋊#101 | 2 |
| M16×#10621924 | 2 |
| #26012370 | 2 |
| #101×D173 | 2 |
| C4×#101 | 173 |