Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 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. #26012220 | C2 | semidirect |
| 3. #26011854 | C2 | semidirect |
| 4. #26011837 | C2 | semidirect |
| 5. #26011789 | C2 | semidirect |
| 6. #26011772 | C2 | semidirect |
| 7. #26011689 | C2 | semidirect |
| 8. #26011618 | C2 | semidirect |
| 9. #26011592 | C2 | semidirect |
| 10. C4×#14583813 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 91. Q8×C173 | #41 | semidirect |
| 124. C173 | #3368 | semidirect |
| 133. #460 | D173 | semidirect |
| 204. Q8 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012220 | 2 |
| #26012161 | 2 |
| #26011854 | 2 |
| #26011837 | 2 |
| #26011789 | 2 |
| #26011772 | 2 |
| #26011689 | 2 |
| #26011618 | 2 |
| #26011592 | 2 |
| C4×#14583813 | 2 |
| #460×C173 | 2 |
| #3368 | 173 |