Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22581464 | C2 | semidirect |
| 3. #22581211 | C2 | semidirect |
| 4. #22581206 | C2 | semidirect |
| 5. #22581199 | C2 | semidirect |
| 6. #22580991 | C2 | semidirect |
| 7. #22580950 | C2 | semidirect |
| 8. C22×M16×C139 | C2 | semidirect |
| 11. C2×Dic556 | C22 | semidirect |
| 12. C2×#14555774 | C22 | semidirect |
| 13. C2×D1112 | C22 | semidirect |
| 20. #17984776 | C22 | semidirect |
| 21. #17984774 | C22 | semidirect |
| 22. #17984767 | C22 | semidirect |
| 23. #17984764 | C22 | semidirect |
| 56. C2×C8×C139 | D4 | semidirect |
| 105. C139 | #3054 | semidirect |
| 108. C22×M16 | D139 | semidirect |
| 156. 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 |
| #22581464 | 2 |
| #22581211 | 2 |
| #22581206 | 2 |
| #22581199 | 2 |
| #22580991 | 2 |
| #22580950 | 2 |
| C22×M16×C139 | 2 |
| #3054 | 139 |