Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012198 | C2 | semidirect |
| 2. #26012161 | C2 | semidirect |
| 3. #26011854 | C2 | semidirect |
| 4. #26011837 | C2 | semidirect |
| 5. #26011793 | C2 | semidirect |
| 6. #26011782 | C2 | semidirect |
| 7. #26011684 | C2 | semidirect |
| 8. #26011618 | C2 | semidirect |
| 9. #26011603 | C2 | semidirect |
| 10. C4×#14583811 | C2 | semidirect |
| 11. #459×C173 | C2 | semidirect |
| 97. D4×C173 | #41 | semidirect |
| 129. C173 | #3366 | semidirect |
| 138. #459 | D173 | semidirect |
| 218. D4 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012198 | 2 |
| #26012161 | 2 |
| #26011854 | 2 |
| #26011837 | 2 |
| #26011793 | 2 |
| #26011782 | 2 |
| #26011684 | 2 |
| #26011618 | 2 |
| #26011603 | 2 |
| C4×#14583811 | 2 |
| #459×C173 | 2 |
| #3366 | 173 |