Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 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. #26012119 | C2 | semidirect |
| 4. #26011259 | C2 | semidirect |
| 5. #26011252 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 49. C2×D4×C173 | Q8 | semidirect |
| 112. C173 | #2027 | semidirect |
| 145. C2×D4 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26011496 | 2 |
| #26011394 | 2 |
| #26011259 | 2 |
| #26011252 | 2 |
| #26011250 | 2 |
| #418×C173 | 2 |
| #2027 | 173 |