Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#19149712 | C2 | semidirect |
| 4. #26011649 | C2 | semidirect |
| 5. #26011632 | C2 | semidirect |
| 6. #26011501 | C2 | semidirect |
| 7. #407×C173 | C2 | semidirect |
| 16. C2×Dic692 | C22 | semidirect |
| 17. C2×#14583815 | C22 | semidirect |
| 24. #19149604 | C22 | semidirect |
| 35. C2×Dic346 | D4 | semidirect |
| 93. C22×C173 | #137 | semidirect |
| 108. C173 | #3004 | semidirect |
| 116. #407 | D173 | semidirect |
| 204. C22 | #19149712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic346 | 2 |
| C2×#19149712 | 2 |
| #26012002 | 2 |
| #26011649 | 2 |
| #26011632 | 2 |
| #26011501 | 2 |
| #407×C173 | 2 |
| #3004 | 173 |