Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #26012214 | C2 | semidirect |
| 2. #26011853 | C2 | semidirect |
| 3. #26011843 | C2 | semidirect |
| 4. #26011783 | C2 | semidirect |
| 5. #26011768 | C2 | semidirect |
| 7. #26011696 | C2 | semidirect |
| 8. #26011622 | C2 | semidirect |
| 9. #26011591 | C2 | semidirect |
| 11. D4×Q8×C173 | C2 | semidirect |
| 122. C173 | #3367 | semidirect |
| 125. D4×Q8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012214 | 2 |
| #26011853 | 2 |
| #26011843 | 2 |
| #26011783 | 2 |
| #26011768 | 2 |
| #26011706 | 2 |
| #26011696 | 2 |
| #26011622 | 2 |
| #26011591 | 2 |
| C4×#14583811 | 2 |
| D4×Q8×C173 | 2 |
| #3367 | 173 |