Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 3. #26012498 | C2 | semidirect |
| 4. #26012497 | C2 | semidirect |
| 5. #26012496 | C2 | semidirect |
| 6. #26012495 | C2 | semidirect |
| 17. #19149746 | C22 | semidirect |
| 18. C4⋊#13063443 | C22 | semidirect |
| 101. C173 | #2905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583836 | 2 |
| C2×D173⋊M16 | 2 |
| #26012498 | 2 |
| #26012497 | 2 |
| #26012496 | 2 |
| #26012495 | 2 |
| #117×D173 | 2 |
| #2905 | 173 |