Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
598 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 76 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×C22⋊#10621924 | C2 | semidirect |
| 2. C2×#19149737 | C2 | semidirect |
| 3. #26012432 | C2 | semidirect |
| 4. #26012369 | C2 | semidirect |
| 15. C22×C22⋊D173 | C4 | semidirect |
| 21. C2×C22⋊Dic173 | C4 | semidirect |
| 22. C2×#14583803 | C4 | semidirect |
| 24. C22×D4×C173 | C4 | semidirect |
| 36. C22⋊#10621924 | D4 | semidirect |
| 54. C22×Dic173 | C2×C4 | semidirect |
| 55. C22×Dic173 | C2×C4 | semidirect |
| 63. C24×C173 | C2×C4 | semidirect |
| 67. C22×C4×C173 | C2×C4 | semidirect |
| 137. C22×C173 | #99 | semidirect |
| 158. C2×D173 | #99 | semidirect |
| 179. C173 | #1898 | semidirect |
| 189. C22×D4 | #10621924 | semidirect |
| 216. C24 | C2×#10621924 | semidirect |
| 234. C22×C4 | C2×#10621924 | semidirect |
| 339. C22 | #19149737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10621924 | 2 |
| C2×#19149737 | 2 |
| #26012432 | 2 |
| #26012369 | 2 |
| C2×#19149647 | 2 |
| #1898 | 173 |