Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26012039 | C2 | semidirect |
| 2. C4×#14583827 | C2 | semidirect |
| 3. #26011813 | C2 | semidirect |
| 4. #26011776 | C2 | semidirect |
| 5. #26011772 | C2 | semidirect |
| 6. #26011683 | C2 | semidirect |
| 7. #26011635 | C2 | semidirect |
| 8. #26011600 | C2 | semidirect |
| 9. #26011592 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #460×C173 | C2 | semidirect |
| 88. D692 | #41 | semidirect |
| 106. Q8×C173 | #41 | semidirect |
| 144. C173 | #3115 | semidirect |
| 151. #460 | D173 | semidirect |
| 233. Q8 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| C4×#14583827 | 2 |
| #26011813 | 2 |
| #26011776 | 2 |
| #26011772 | 2 |
| #26011683 | 2 |
| #26011635 | 2 |
| #26011600 | 2 |
| #26011592 | 2 |
| #26011547 | 2 |
| #460×C173 | 2 |
| #3115 | 173 |