Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 67 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. C8×Dic346 | C2 | semidirect |
| 4. #26011242 | C2 | semidirect |
| 5. #26011223 | C2 | semidirect |
| 7. #322×C173 | C2 | semidirect |
| 43. Dic346 | M16 | semidirect |
| 60. C8×C173 | SD16 | semidirect |
| 77. C173 | #1583 | semidirect |
| 85. #322 | D173 | semidirect |
| 138. C8 | #14583815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic346 | 2 |
| C4×#14583815 | 2 |
| #26011570 | 2 |
| #26011242 | 2 |
| #26011223 | 2 |
| #26011220 | 2 |
| #322×C173 | 2 |
| #1583 | 173 |