Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 186 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. #26012543 | C2 | direct (N × H) |
| 31. C2×#13063443 | Q8 | semidirect |
| 57. #13063443 | C2×Q8 | semidirect |
| 89. C2×C173 | #446 | semidirect |
| 93. C173 | C2×#446 | semidirect |
| 183. C2 | #26012543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012543 | 2 |
| C2×#19149746 | 2 |
| C2×C4⋊#13063443 | 2 |
| C2×#19149734 | 2 |
| C2×C4×#13063443 | 2 |
| C2×#19149644 | 2 |
| C2×#446 | 173 |