Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×#19149644 | C2 | semidirect |
| 4. #26011588 | C2 | direct (N × H) |
| 5. C2×#19149612 | C2 | semidirect |
| 6. C2×#19149604 | C2 | semidirect |
| 7. C2×#19149589 | C2 | semidirect |
| 11. C2×#14583814 | C4 | semidirect |
| 15. #19149644 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149604 | C22 | semidirect |
| 25. #19149589 | C22 | semidirect |
| 32. C2×Dic346 | C2×C4 | semidirect |
| 40. #14583814 | C2×C4 | semidirect |
| 41. C2×#13063436 | C2×C4 | semidirect |
| 63. Dic346 | C22×C4 | semidirect |
| 73. #13063436 | C22×C4 | semidirect |
| 106. C2×C173 | #440 | semidirect |
| 110. C173 | C2×#440 | semidirect |
| 217. C2 | #26011588 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583814 | 2 |
| C2×#19149644 | 2 |
| C2×D4×Dic173 | 2 |
| #26011588 | 2 |
| C2×#19149612 | 2 |
| C2×#19149604 | 2 |
| C2×#19149589 | 2 |
| C2×#102×C173 | 2 |
| C2×#440 | 173 |