Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26011622 | C2 | semidirect |
| 4. #26011241 | C2 | semidirect |
| 6. #26011213 | C2 | semidirect |
| 7. Q8⋊C8×C173 | C2 | semidirect |
| 51. #13063436 | SD16 | semidirect |
| 77. C173 | #1582 | semidirect |
| 83. Q8⋊C8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011622 | 2 |
| C4×#14583813 | 2 |
| #26011556 | 2 |
| #26011241 | 2 |
| #26011220 | 2 |
| #26011213 | 2 |
| Q8⋊C8×C173 | 2 |
| #1582 | 173 |