Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26011837 | C2 | semidirect |
| 3. #26011772 | C2 | semidirect |
| 4. #26011697 | C2 | semidirect |
| 5. #26011218 | C2 | semidirect |
| 6. #26011218 | C2 | semidirect |
| 7. #331×C173 | C2 | semidirect |
| 11. #19149679 | C22 | semidirect |
| 21. C4×#13063436 | C22 | semidirect |
| 23. C4⋊C8×C173 | C22 | semidirect |
| 24. C4⋊C8×C173 | C22 | semidirect |
| 62. D692 | SD16 | semidirect |
| 109. C173 | #1639 | semidirect |
| 115. #331 | D173 | semidirect |
| 129. C4⋊C8 | C2×D173 | semidirect |
| 130. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012126 | 2 |
| #26011837 | 2 |
| #26011772 | 2 |
| #26011697 | 2 |
| #26011218 | 2 |
| #331×C173 | 2 |
| #1639 | 173 |