Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #26011243 | C2 | semidirect |
| 5. #26011242 | C2 | semidirect |
| 6. #26011241 | C2 | semidirect |
| 7. #335×C173 | C2 | semidirect |
| 53. #13063436 | M16 | semidirect |
| 60. C8×C173 | M16 | semidirect |
| 77. C173 | #1569 | semidirect |
| 83. #335 | D173 | semidirect |
| 138. C8 | #14583809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011547 | 2 |
| #26011513 | 2 |
| C4×#14583809 | 2 |
| #26011243 | 2 |
| #26011242 | 2 |
| #26011241 | 2 |
| #335×C173 | 2 |
| #1569 | 173 |