Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 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. #26012048 | C2 | semidirect |
| 2. #26011901 | C2 | semidirect |
| 3. #26011886 | C2 | semidirect |
| 4. #26011861 | C2 | semidirect |
| 5. #26011850 | C2 | semidirect |
| 6. #26011747 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 9. C4×#14583814 | C2 | semidirect |
| 10. C4×#14583810 | C2 | semidirect |
| 129. C173 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26011901 | 2 |
| #26011886 | 2 |
| #26011861 | 2 |
| #26011850 | 2 |
| #26011747 | 2 |
| #26011735 | 2 |
| C4×#14583816 | 2 |
| C4×#14583814 | 2 |
| C4×#14583810 | 2 |
| #529×C173 | 2 |
| #3172 | 173 |