Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26011838 | C2 | semidirect |
| 2. #26011781 | C2 | semidirect |
| 4. #26011242 | C2 | semidirect |
| 5. #26011239 | C2 | semidirect |
| 6. #26011234 | C2 | semidirect |
| 7. C8×D4×C173 | C2 | semidirect |
| 82. C173 | #1677 | semidirect |
| 87. C8×D4 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011838 | 2 |
| #26011781 | 2 |
| #26011686 | 2 |
| #26011242 | 2 |
| #26011239 | 2 |
| #26011234 | 2 |
| C8×D4×C173 | 2 |
| #1677 | 173 |