Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
560 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 233 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. #26011384 | C2 | semidirect |
| 3. #26011357 | C2 | semidirect |
| 4. #26011354 | C2 | semidirect |
| 5. C4⋊C4×Dic173 | C2 | semidirect |
| 6. C4×C4⋊Dic173 | C2 | semidirect |
| 7. C4×C22⋊Dic173 | C2 | semidirect |
| 22. C4×D4×C173 | C4 | semidirect |
| 97. C173 | #2357 | semidirect |
| 109. 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 |
| #26011384 | 2 |
| #26011357 | 2 |
| #26011354 | 2 |
| C4⋊C4×Dic173 | 2 |
| C4×C4⋊Dic173 | 2 |
| C4×C22⋊Dic173 | 2 |
| C2×C4×D4×C173 | 2 |
| #2357 | 173 |