Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#17984889 | C2 | semidirect |
| 2. C22×#14555773 | C2 | semidirect |
| 3. #22581520 | C2 | semidirect |
| 4. #22581095 | C2 | semidirect |
| 5. #22581090 | C2 | semidirect |
| 6. #22580963 | C2 | semidirect |
| 7. #22580949 | C2 | semidirect |
| 8. #22580921 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C139 | C2 | semidirect |
| 15. C2×#14555784 | C22 | semidirect |
| 18. C2×Q8×D139 | C22 | semidirect |
| 27. #17984767 | C22 | semidirect |
| 28. #17984766 | C22 | semidirect |
| 29. #17984763 | C22 | semidirect |
| 30. (C2×D139)⋊C8 | C22 | semidirect |
| 48. C2×Dic278 | D4 | semidirect |
| 69. #41×C139 | D4 | semidirect |
| 145. C139 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D139 | semidirect |
| 191. #41 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| C22×#14555773 | 2 |
| #22581520 | 2 |
| #22581095 | 2 |
| #22581090 | 2 |
| #22580963 | 2 |
| #22580949 | 2 |
| #22580921 | 2 |
| C2×AGL(1,ℤ/8)×C139 | 2 |
| #3010 | 139 |