Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
540 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 229 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. #26011390 | C2 | semidirect |
| 3. #26011384 | C2 | semidirect |
| 4. #26011354 | C2 | semidirect |
| 5. #26011351 | C2 | semidirect |
| 6. C4×C4⋊Dic173 | C2 | semidirect |
| 7. #26011337 | C2 | semidirect |
| 22. C4×D4×C173 | C4 | semidirect |
| 96. C173 | #2319 | semidirect |
| 108. C4×D4 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011394 | 2 |
| #26011390 | 2 |
| #26011384 | 2 |
| #26011354 | 2 |
| #26011351 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011337 | 2 |
| C2×C4×D4×C173 | 2 |
| #2319 | 173 |