Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22581430 | C2 | semidirect |
| 4. #22581050 | C2 | semidirect |
| 5. #22581044 | C2 | semidirect |
| 6. #22580989 | C2 | semidirect |
| 7. #22580963 | C2 | semidirect |
| 8. #22580911 | C2 | semidirect |
| 11. C2×#14555773 | C4 | semidirect |
| 16. #17984807 | C22 | semidirect |
| 23. #17984775 | C22 | semidirect |
| 24. #17984773 | C22 | semidirect |
| 25. #17984767 | C22 | semidirect |
| 26. #17984752 | C22 | semidirect |
| 27. C8×Dic139 | C22 | semidirect |
| 34. C2×Dic278 | C2×C4 | semidirect |
| 38. #14555773 | C2×C4 | semidirect |
| 39. #14555773 | C2×C4 | semidirect |
| 40. C2×C139⋊C8 | C2×C4 | semidirect |
| 103. C139 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555773 | 2 |
| #22581430 | 2 |
| #22581428 | 2 |
| #22581050 | 2 |
| #22581044 | 2 |
| #22580989 | 2 |
| #22580963 | 2 |
| #22580911 | 2 |
| #418×C139 | 2 |
| #2949 | 139 |