Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
260 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 12. #19149746 | C4 | semidirect |
| 13. C4⋊#13063443 | C4 | semidirect |
| 21. C4⋊#13063436 | C4 | semidirect |
| 22. #19149608 | C4 | semidirect |
| 23. #19149608 | C4 | semidirect |
| 24. C4⋊C8×C173 | C4 | semidirect |
| 97. C173 | #1768 | semidirect |
| 118. C4⋊C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C4⋊C8) | 2 |
| C2×#19149733 | 2 |
| C2×C8×#10621924 | 2 |
| #26012427 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| C4⋊C8×D173 | 2 |
| #1768 | 173 |