Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
604 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 237 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. #26011431 | C2 | direct (N × H) |
| 77. C2×C173 | #400 | semidirect |
| 83. C173 | C2×#400 | semidirect |
| 161. C2 | #26011431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic173 | 2 |
| C22×#14583805 | 2 |
| #26011431 | 2 |
| C2×#19149586 | 2 |
| C2×#95×C173 | 2 |
| C2×#400 | 173 |