Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26011900 | C2 | semidirect |
| 3. #26011893 | C2 | semidirect |
| 4. #26011889 | C2 | semidirect |
| 40. M16×C173 | Q8 | semidirect |
| 41. C2×C8×C173 | Q8 | semidirect |
| 75. C173 | #3163 | semidirect |
| 107. M16 | Dic346 | semidirect |
| 108. C2×C8 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26011900 | 2 |
| #26011893 | 2 |
| #26011889 | 2 |
| #26011533 | 2 |
| #26011529 | 2 |
| C2×#19149611 | 2 |
| #405×C173 | 2 |
| #3163 | 173 |