Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581584 | C2 | semidirect |
| 3. #22581320 | C2 | semidirect |
| 4. #22581314 | C2 | semidirect |
| 5. #22581309 | C2 | semidirect |
| 6. #22581302 | C2 | semidirect |
| 7. #22580962 | C2 | semidirect |
| 10. #22580908 | C2 | semidirect |
| 11. C2×#103×C139 | C2 | semidirect |
| 127. C139 | #3137 | semidirect |
| 138. C2×#103 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22581527 | 2 |
| #22581320 | 2 |
| #22581314 | 2 |
| #22581309 | 2 |
| #22581302 | 2 |
| #22580962 | 2 |
| #22580952 | 2 |
| #22580950 | 2 |
| #22580908 | 2 |
| C2×#103×C139 | 2 |
| #3137 | 139 |