Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #26011972 | C2 | semidirect |
| 3. C2×#19149605 | C2 | semidirect |
| 4. #26011497 | C2 | semidirect |
| 5. #26011392 | C2 | semidirect |
| 6. #26011252 | C2 | semidirect |
| 7. #343×C173 | C2 | semidirect |
| 11. #19149707 | C4 | semidirect |
| 39. C2×D692 | C2×C4 | semidirect |
| 62. M16×C173 | C2×C4 | semidirect |
| 74. Dic346 | C22⋊C4 | semidirect |
| 80. D692 | C22⋊C4 | semidirect |
| 132. C173 | #1883 | semidirect |
| 139. #343 | D173 | semidirect |
| 185. M16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| #26011972 | 2 |
| C2×#19149605 | 2 |
| #26011497 | 2 |
| #26011392 | 2 |
| #26011252 | 2 |
| #343×C173 | 2 |
| #1883 | 173 |