Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #26011841 | C2 | semidirect |
| 3. #26011776 | C2 | semidirect |
| 5. Q8×#13063436 | C2 | semidirect |
| 7. #557×C173 | C2 | semidirect |
| 53. Q8×C173 | SD16 | semidirect |
| 74. C173 | #3359 | semidirect |
| 76. #557 | D173 | semidirect |
| 122. Q8 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D692 | 2 |
| #26011841 | 2 |
| #26011776 | 2 |
| #26011693 | 2 |
| Q8×#13063436 | 2 |
| C4×#14583813 | 2 |
| #557×C173 | 2 |
| #3359 | 173 |