Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
432 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 141 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. C173⋊#401 | C2 | semidirect |
| 2. #26011432 | C2 | semidirect |
| 5. C4×#14583805 | C2 | semidirect |
| 7. #376×C173 | C2 | semidirect |
| 70. C173 | #2401 | semidirect |
| 78. #376 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C173⋊#401 | 2 |
| #26011432 | 2 |
| #26011420 | 2 |
| #26011415 | 2 |
| C4×#14583805 | 2 |
| C4×#14583803 | 2 |
| #376×C173 | 2 |
| #2401 | 173 |