Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 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. #26011527 | C2 | semidirect |
| 3. #26011509 | C2 | semidirect |
| 4. #26011508 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #26011447 | C2 | semidirect |
| 7. #410×C173 | C2 | semidirect |
| 13. C2×#14583816 | C4 | semidirect |
| 14. C2×#14583814 | C4 | semidirect |
| 15. C2×#14583813 | C4 | semidirect |
| 16. C2×#14583811 | C4 | semidirect |
| 132. C173 | #1976 | semidirect |
| 139. #410 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149699 | 2 |
| #26011527 | 2 |
| #26011509 | 2 |
| #26011508 | 2 |
| #26011464 | 2 |
| #26011447 | 2 |
| #410×C173 | 2 |
| #1976 | 173 |