Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #22581719 | C2 | semidirect |
| 3. #22581076 | C2 | semidirect |
| 4. #22581071 | C2 | semidirect |
| 5. #22581002 | C2 | semidirect |
| 6. C2×#17984770 | C2 | semidirect |
| 7. C4×M16×C139 | C2 | semidirect |
| 9. #17984875 | C4 | semidirect |
| 10. #17984870 | C4 | semidirect |
| 13. #17984848 | C22 | semidirect |
| 16. #17984778 | C22 | semidirect |
| 17. #17984770 | C22 | semidirect |
| 18. #17984770 | C22 | semidirect |
| 22. #97×C139 | C22 | semidirect |
| 23. C4×C8×C139 | C22 | semidirect |
| 32. Dic556 | C2×C4 | semidirect |
| 33. #14555774 | C2×C4 | semidirect |
| 34. D1112 | C2×C4 | semidirect |
| 85. C139 | #2956 | semidirect |
| 93. C4×M16 | D139 | semidirect |
| 108. #97 | C2×D139 | semidirect |
| 109. C4×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581753 | 2 |
| #22581719 | 2 |
| #22581076 | 2 |
| #22581071 | 2 |
| #22581002 | 2 |
| C2×#17984770 | 2 |
| C4×M16×C139 | 2 |
| #2956 | 139 |