Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26011544 | C2 | semidirect |
| 3. #26011216 | C2 | semidirect |
| 5. #431×C173 | C2 | semidirect |
| 30. C2×C4×D173 | C8 | semidirect |
| 102. C173 | #1458 | semidirect |
| 106. #431 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149636 | 2 |
| #26011544 | 2 |
| #26011216 | 2 |
| #26011214 | 2 |
| #431×C173 | 2 |
| #1458 | 173 |