Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26012038 | C2 | semidirect |
| 2. #26011895 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011728 | C2 | semidirect |
| 6. #26011726 | C2 | semidirect |
| 7. #26011724 | C2 | semidirect |
| 8. C4×D1384 | C2 | semidirect |
| 9. C4×#14583811 | C2 | semidirect |
| 10. C4×C8×D173 | C2 | semidirect |
| 11. C4×D8×C173 | C2 | semidirect |
| 89. C4×D173 | D8 | semidirect |
| 91. #13063436 | #41 | semidirect |
| 101. C8×C173 | #41 | semidirect |
| 127. C173 | #3169 | semidirect |
| 138. C4×D8 | D173 | semidirect |
| 229. C8 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012038 | 2 |
| #26011895 | 2 |
| #26011866 | 2 |
| #26011836 | 2 |
| #26011728 | 2 |
| #26011726 | 2 |
| #26011724 | 2 |
| C4×D1384 | 2 |
| C4×#14583811 | 2 |
| C4×C8×D173 | 2 |
| C4×D8×C173 | 2 |
| #3169 | 173 |