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. #22581431 | C2 | semidirect |
| 4. #22581056 | C2 | semidirect |
| 5. #22581038 | C2 | semidirect |
| 6. #22580989 | C2 | semidirect |
| 8. #22580911 | C2 | semidirect |
| 9. #419×C139 | C2 | semidirect |
| 11. C2×#14555772 | C4 | semidirect |
| 16. Q8×Dic139 | C22 | semidirect |
| 23. #17984775 | C22 | semidirect |
| 24. #17984773 | C22 | semidirect |
| 26. #17984752 | C22 | semidirect |
| 27. C8×Dic139 | C22 | semidirect |
| 31. #103×C139 | C22 | semidirect |
| 38. #14555772 | C2×C4 | semidirect |
| 39. #14555772 | C2×C4 | semidirect |
| 40. C2×C139⋊C8 | C2×C4 | semidirect |
| 54. C2×Q8×C139 | C2×C4 | semidirect |
| 103. C139 | #2949 | semidirect |
| 111. #419 | D139 | semidirect |
| 132. #103 | C2×D139 | semidirect |
| 139. C2×Q8 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555772 | 2 |
| #22581431 | 2 |
| #22581427 | 2 |
| #22581056 | 2 |
| #22581038 | 2 |
| #22580989 | 2 |
| #22580959 | 2 |
| #22580911 | 2 |
| #419×C139 | 2 |
| #2949 | 139 |