Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012214 | C2 | semidirect |
| 3. #26011838 | C2 | semidirect |
| 4. #26011818 | C2 | semidirect |
| 5. #26011776 | C2 | semidirect |
| 6. #26011723 | C2 | semidirect |
| 7. #26011691 | C2 | semidirect |
| 8. #26011652 | C2 | semidirect |
| 9. C8×D692 | C2 | semidirect |
| 10. #26011486 | C2 | semidirect |
| 11. C4×Q16×C173 | C2 | semidirect |
| 127. C173 | #3304 | semidirect |
| 137. C4×Q16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012214 | 2 |
| #26012163 | 2 |
| #26011838 | 2 |
| #26011818 | 2 |
| #26011776 | 2 |
| #26011723 | 2 |
| #26011691 | 2 |
| #26011652 | 2 |
| C8×D692 | 2 |
| #26011486 | 2 |
| C4×Q16×C173 | 2 |
| #3304 | 173 |