Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #26011899 | C2 | semidirect |
| 4. #26011894 | C2 | semidirect |
| 5. #26011889 | C2 | semidirect |
| 6. #26011887 | C2 | semidirect |
| 9. #500×C173 | C2 | semidirect |
| 43. #14583809 | Q8 | semidirect |
| 79. #13063436 | C2×Q8 | semidirect |
| 87. C8×C173 | C2×Q8 | semidirect |
| 106. C173 | #3165 | semidirect |
| 112. #500 | D173 | semidirect |
| 194. C8 | Q8×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011899 | 2 |
| #26011894 | 2 |
| #26011889 | 2 |
| #26011887 | 2 |
| #26011532 | 2 |
| C4×#14583809 | 2 |
| #500×C173 | 2 |
| #3165 | 173 |