Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26011839 | C2 | semidirect |
| 3. #26011815 | C2 | semidirect |
| 4. #26011773 | C2 | semidirect |
| 5. #26011722 | C2 | semidirect |
| 6. #26011691 | C2 | semidirect |
| 7. #26011651 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 9. D4×#13063436 | C2 | semidirect |
| 10. #26011485 | C2 | semidirect |
| 11. #556×C173 | C2 | semidirect |
| 127. C173 | #3304 | semidirect |
| 129. #556 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012162 | 2 |
| #26011839 | 2 |
| #26011815 | 2 |
| #26011773 | 2 |
| #26011722 | 2 |
| #26011691 | 2 |
| #26011651 | 2 |
| C4×#14583816 | 2 |
| D4×#13063436 | 2 |
| #26011485 | 2 |
| #556×C173 | 2 |
| #3304 | 173 |