Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012219 | C2 | semidirect |
| 3. #26011842 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 5. #26011776 | C2 | semidirect |
| 6. #26011775 | C2 | semidirect |
| 9. C8×Dic346 | C2 | semidirect |
| 78. Dic346 | SD16 | semidirect |
| 118. C173 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012219 | 2 |
| D4×Dic346 | 2 |
| #26011842 | 2 |
| #26011840 | 2 |
| #26011776 | 2 |
| #26011775 | 2 |
| #26011696 | 2 |
| #26011694 | 2 |
| C8×Dic346 | 2 |
| #26011582 | 2 |
| C4×SD16×C173 | 2 |
| #3359 | 173 |