Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #22581427 | C2 | semidirect |
| 3. #22581066 | C2 | semidirect |
| 4. C4×D1112 | C2 | semidirect |
| 5. #22580991 | C2 | semidirect |
| 6. #22580959 | C2 | semidirect |
| 7. #405×C139 | C2 | semidirect |
| 9. C2×D1112 | C4 | semidirect |
| 12. C4×D556 | C22 | semidirect |
| 16. #17984776 | C22 | semidirect |
| 17. #17984774 | C22 | semidirect |
| 18. #17984764 | C22 | semidirect |
| 22. #97×C139 | C22 | semidirect |
| 23. C4×C8×C139 | C22 | semidirect |
| 27. C2×D556 | C2×C4 | semidirect |
| 30. D1112 | C2×C4 | semidirect |
| 31. D1112 | C2×C4 | semidirect |
| 38. C2×C8×C139 | C2×C4 | semidirect |
| 77. C139 | #2948 | semidirect |
| 85. #405 | D139 | semidirect |
| 100. #97 | C2×D139 | semidirect |
| 101. C4×C8 | C2×D139 | semidirect |
| 112. C2×C8 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1112 | 2 |
| #22581427 | 2 |
| #22581066 | 2 |
| C4×D1112 | 2 |
| #22580991 | 2 |
| #22580959 | 2 |
| #405×C139 | 2 |
| #2948 | 139 |