Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic346 | C2 | semidirect |
| 2. C22×#14583814 | C2 | semidirect |
| 3. #26011629 | C2 | direct (N × H) |
| 4. C2×#19149602 | C2 | semidirect |
| 5. C2×C22⋊#13063436 | C2 | semidirect |
| 11. C22×Dic346 | C22 | semidirect |
| 14. C2×#14583814 | C22 | semidirect |
| 16. #19149602 | C22 | semidirect |
| 17. C22⋊#13063436 | C22 | semidirect |
| 31. C2×Dic346 | D4 | semidirect |
| 58. Dic346 | C2×D4 | semidirect |
| 69. C23×C173 | SD16 | semidirect |
| 93. C22×C173 | C2×SD16 | semidirect |
| 103. C2×C173 | #448 | semidirect |
| 107. C173 | C2×#448 | semidirect |
| 169. C23 | #14583814 | semidirect |
| 201. C22 | C2×#14583814 | semidirect |
| 211. C2 | #26011629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic346 | 2 |
| C22×#14583814 | 2 |
| #26011629 | 2 |
| C2×#19149602 | 2 |
| C2×C22⋊#13063436 | 2 |
| C2×#121×C173 | 2 |
| C2×#448 | 173 |