Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26011965 | C2 | semidirect |
| 3. #26011508 | C2 | semidirect |
| 4. #26011495 | C2 | semidirect |
| 5. #26011261 | C2 | semidirect |
| 6. #26011247 | C2 | semidirect |
| 7. #410×C173 | C2 | semidirect |
| 11. C2×#14583813 | C4 | semidirect |
| 12. C2×#14583811 | C4 | semidirect |
| 40. C2×#13063436 | C2×C4 | semidirect |
| 49. C2×Q8×C173 | C2×C4 | semidirect |
| 51. C2×D4×C173 | C2×C4 | semidirect |
| 115. C173 | #1904 | semidirect |
| 121. #410 | D173 | semidirect |
| 146. C2×Q8 | C4×D173 | semidirect |
| 154. C2×D4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| #26011965 | 2 |
| #26011508 | 2 |
| #26011495 | 2 |
| #26011261 | 2 |
| #26011247 | 2 |
| #410×C173 | 2 |
| #1904 | 173 |