Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26011309 | C2 | semidirect |
| 4. C4×#14583801 | C2 | semidirect |
| 5. #346×C173 | C2 | semidirect |
| 50. C173 | #2164 | semidirect |
| 55. #346 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011445 | 2 |
| #26011309 | 2 |
| #26011270 | 2 |
| C4×#14583801 | 2 |
| #346×C173 | 2 |
| #2164 | 173 |