Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 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. #26012522 | C2 | semidirect |
| 2. #26012511 | C2 | semidirect |
| 3. #26012461 | C2 | semidirect |
| 4. C2×C22⋊#13063443 | C2 | semidirect |
| 6. C2×#14583835 | C22 | semidirect |
| 7. C22×#13063443 | C22 | semidirect |
| 8. #19149746 | C22 | semidirect |
| 10. C22⋊#13063443 | C22 | semidirect |
| 11. C22⋊#13063443 | C22 | semidirect |
| 12. #19149734 | C22 | semidirect |
| 64. C23×C173 | M16 | semidirect |
| 95. C173 | #2973 | semidirect |
| 146. C23 | #14583835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012522 | 2 |
| #26012511 | 2 |
| #26012461 | 2 |
| C2×C22⋊#13063443 | 2 |
| C2×D4×Dic173 | 2 |
| #2973 | 173 |