Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×D692 | C2 | semidirect |
| 2. #26011837 | C2 | semidirect |
| 4. #26011238 | C2 | semidirect |
| 5. Q8⋊#13063436 | C2 | semidirect |
| 6. #26011218 | C2 | semidirect |
| 7. #460×C173 | C2 | semidirect |
| 56. D692 | SD16 | semidirect |
| 66. Q8×C173 | D8 | semidirect |
| 99. C173 | #1627 | semidirect |
| 103. #460 | D173 | semidirect |
| 157. Q8 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D692 | 2 |
| #26011837 | 2 |
| #26011683 | 2 |
| #26011238 | 2 |
| Q8⋊#13063436 | 2 |
| #26011218 | 2 |
| #460×C173 | 2 |
| #1627 | 173 |