Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26012044 | C2 | semidirect |
| 4. #26011261 | C2 | semidirect |
| 5. #26011250 | C2 | semidirect |
| 6. #26011247 | C2 | semidirect |
| 44. C2×Q8×C173 | Q8 | semidirect |
| 46. C2×D4×C173 | Q8 | semidirect |
| 102. C173 | #2031 | semidirect |
| 131. C2×Q8 | Dic346 | semidirect |
| 133. C2×D4 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| #26011508 | 2 |
| C2×#19149606 | 2 |
| #26011261 | 2 |
| #26011250 | 2 |
| #26011247 | 2 |
| #410×C173 | 2 |
| #2031 | 173 |