Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 2. #26012442 | C2 | semidirect |
| 3. #26012441 | C2 | semidirect |
| 4. #26012434 | C2 | semidirect |
| 5. #26012433 | C2 | semidirect |
| 6. C4×C4⋊#10621924 | C2 | semidirect |
| 7. #26012427 | C2 | semidirect |
| 22. C4×D692 | C4 | semidirect |
| 23. D4×Dic173 | C4 | semidirect |
| 24. #19149641 | C4 | semidirect |
| 25. C4×C22⋊D173 | C4 | semidirect |
| 26. #19149639 | C4 | semidirect |
| 30. C4×D4×C173 | C4 | semidirect |
| 132. C173 | #2319 | semidirect |
| 149. C4×D4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012443 | 2 |
| #26012442 | 2 |
| #26012441 | 2 |
| #26012434 | 2 |
| #26012433 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012427 | 2 |
| C4×D4×D173 | 2 |
| #2319 | 173 |