Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. #26011858 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 100. C173 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| C2×#19149677 | 2 |
| #26011858 | 2 |
| #26011840 | 2 |
| #26011501 | 2 |
| #26011500 | 2 |
| #26011499 | 2 |
| M16×Dic173 | 2 |
| #419×C173 | 2 |
| #3139 | 173 |