Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26011570 | C2 | semidirect |
| 3. #26011243 | C2 | semidirect |
| 4. D4⋊#13063436 | C2 | semidirect |
| 5. #26011218 | C2 | semidirect |
| 6. C8×#13063436 | C2 | semidirect |
| 7. #436×C173 | C2 | semidirect |
| 51. #13063436 | M16 | semidirect |
| 63. C8×C173 | D8 | semidirect |
| 83. C173 | #1589 | semidirect |
| 87. #436 | D173 | semidirect |
| 147. C8 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583811 | 2 |
| #26011570 | 2 |
| #26011243 | 2 |
| D4⋊#13063436 | 2 |
| #26011218 | 2 |
| C8×#13063436 | 2 |
| #436×C173 | 2 |
| #1589 | 173 |