Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26012291 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. #26012058 | C2 | semidirect |
| 4. #26011509 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #26011262 | C2 | semidirect |
| 7. #418×C173 | C2 | semidirect |
| 40. C2×Dic346 | D4 | semidirect |
| 42. C2×D692 | D4 | semidirect |
| 55. #14583810 | D4 | semidirect |
| 71. C2×C8×C173 | D4 | semidirect |
| 142. C173 | #2008 | semidirect |
| 148. #418 | D173 | semidirect |
| 210. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012291 | 2 |
| C2×#19149705 | 2 |
| #26012058 | 2 |
| #26011509 | 2 |
| #26011464 | 2 |
| #26011262 | 2 |
| #418×C173 | 2 |
| #2008 | 173 |