Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
228 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 4. C2×D173⋊C8 | C4 | semidirect |
| 9. (C2×#10621924)⋊C4 | C4 | semidirect |
| 13. #19149586 | C4 | semidirect |
| 14. #95×C173 | C4 | semidirect |
| 96. C173 | #1289 | semidirect |
| 111. #95 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C22⋊C8) | 2 |
| #26012433 | 2 |
| #26011350 | 2 |
| #1289 | 173 |