Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14583816 | C2 | semidirect |
| 4. #26011713 | C2 | direct (N × H) |
| 5. C2×C4⋊#13063436 | C2 | semidirect |
| 6. C2×#19149602 | C2 | semidirect |
| 8. C2×C4×Q8×C173 | C2 | semidirect |
| 12. C2×#14583816 | C22 | semidirect |
| 21. C4⋊#13063436 | C22 | semidirect |
| 22. #19149602 | C22 | semidirect |
| 26. C4×Q8×C173 | C22 | semidirect |
| 110. C2×C173 | #464 | semidirect |
| 115. C173 | C2×#464 | semidirect |
| 120. C2×C4×Q8 | D173 | semidirect |
| 137. C4×Q8 | C2×D173 | semidirect |
| 227. C2 | #26011713 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583816 | 2 |
| C22×#14583813 | 2 |
| C2×#19149667 | 2 |
| #26011713 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149602 | 2 |
| C2×#19149599 | 2 |
| C2×C4×Q8×C173 | 2 |
| C2×#464 | 173 |