Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#17984864 | C2 | semidirect |
| 2. C2×#17984862 | C2 | semidirect |
| 3. #22581499 | C2 | semidirect |
| 4. #22581338 | C2 | semidirect |
| 5. #22581336 | C2 | semidirect |
| 6. #22581334 | C2 | semidirect |
| 7. #22581331 | C2 | semidirect |
| 8. #22581328 | C2 | semidirect |
| 9. #22581324 | C2 | semidirect |
| 10. C2×C8×Dic139 | C2 | semidirect |
| 11. C2×#135×C139 | C2 | semidirect |
| 55. C2×C139⋊C8 | D4 | semidirect |
| 74. C2×C8×C139 | D4 | semidirect |
| 119. Dic139 | #135 | semidirect |
| 125. C139 | #3147 | semidirect |
| 129. C2×#135 | D139 | semidirect |
| 194. C2×C8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| C2×#17984862 | 2 |
| #22581499 | 2 |
| #22581338 | 2 |
| #22581336 | 2 |
| #22581334 | 2 |
| #22581331 | 2 |
| #22581328 | 2 |
| #22581324 | 2 |
| C2×C8×Dic139 | 2 |
| C2×#135×C139 | 2 |
| #3147 | 139 |