Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581498 | C2 | semidirect |
| 2. #22581357 | C2 | semidirect |
| 3. #22581328 | C2 | semidirect |
| 4. #22581298 | C2 | semidirect |
| 5. #22581189 | C2 | semidirect |
| 6. #22581187 | C2 | semidirect |
| 7. D8×Dic139 | C2 | semidirect |
| 8. #22581035 | C2 | semidirect |
| 9. #22581033 | C2 | semidirect |
| 10. C2×C8×Dic139 | C2 | semidirect |
| 11. #466×C139 | C2 | semidirect |
| 82. C2×Dic139 | D8 | semidirect |
| 89. C139⋊C8 | #41 | semidirect |
| 101. C8×C139 | #41 | semidirect |
| 127. C139 | #3169 | semidirect |
| 135. #466 | D139 | semidirect |
| 229. C8 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581498 | 2 |
| #22581357 | 2 |
| #22581328 | 2 |
| #22581298 | 2 |
| #22581189 | 2 |
| #22581187 | 2 |
| D8×Dic139 | 2 |
| #22581035 | 2 |
| #22581033 | 2 |
| C2×C8×Dic139 | 2 |
| #466×C139 | 2 |
| #3169 | 139 |