Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 156 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. #26012516 | C2 | semidirect |
| 2. #26012514 | C2 | semidirect |
| 3. #26012509 | C2 | semidirect |
| 4. #26012496 | C2 | semidirect |
| 5. D173⋊(C4⋊C8) | C2 | semidirect |
| 7. #26012456 | C2 | semidirect |
| 108. C173 | #2925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012516 | 2 |
| #26012514 | 2 |
| #26012509 | 2 |
| #26012496 | 2 |
| D173⋊(C4⋊C8) | 2 |
| #26012466 | 2 |
| #26012456 | 2 |
| C4×#14583827 | 2 |
| #2925 | 173 |