Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 153 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. #26011798 | C2 | semidirect |
| 3. #26011786 | C2 | semidirect |
| 4. #26011776 | C2 | semidirect |
| 47. C2×Q8×C173 | Q8 | semidirect |
| 106. C173 | #3078 | semidirect |
| 144. C2×Q8 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26011798 | 2 |
| #26011786 | 2 |
| #26011776 | 2 |
| #26011531 | 2 |
| #26011515 | 2 |
| #26011500 | 2 |
| C2×C4×Q8×C173 | 2 |
| #3078 | 173 |