Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×#19149748 | C2 | semidirect |
| 2. C2×#19149747 | C2 | semidirect |
| 4. #26012365 | C2 | semidirect |
| 13. C2×#14583810 | C4 | semidirect |
| 14. C2×#14583809 | C4 | semidirect |
| 15. C2×#14583809 | C4 | semidirect |
| 20. C2×M16×C173 | C4 | semidirect |
| 78. #13063436 | C22⋊C4 | semidirect |
| 85. C8×C173 | C22⋊C4 | semidirect |
| 113. C173 | #1809 | semidirect |
| 126. C2×M16 | #10621924 | semidirect |
| 199. C8 | C22⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149748 | 2 |
| C2×#19149747 | 2 |
| #26012433 | 2 |
| #26012365 | 2 |
| C2×M16×D173 | 2 |
| #1809 | 173 |