Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#17984867 | C2 | semidirect |
| 2. C22×#14555772 | C2 | semidirect |
| 3. #22581517 | C2 | semidirect |
| 4. #22581098 | C2 | semidirect |
| 5. #22581092 | C2 | semidirect |
| 6. #22580962 | C2 | semidirect |
| 7. #22580949 | C2 | semidirect |
| 8. #22580920 | C2 | semidirect |
| 9. C2×2−1+4×C139 | C2 | semidirect |
| 23. #17984766 | C22 | semidirect |
| 24. #17984766 | C22 | semidirect |
| 25. #17984763 | C22 | semidirect |
| 26. C22⋊(C139⋊C8) | C22 | semidirect |
| 33. C2×#41×C139 | C22 | semidirect |
| 36. C22×Q8×C139 | C22 | semidirect |
| 61. #41×C139 | D4 | semidirect |
| 69. C2×Q8×C139 | D4 | semidirect |
| 145. C139 | #3010 | semidirect |
| 147. C2×2−1+4 | D139 | semidirect |
| 162. C2×#41 | C2×D139 | semidirect |
| 165. C22×Q8 | C2×D139 | semidirect |
| 191. #41 | C22⋊D139 | semidirect |
| 199. C2×Q8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984867 | 2 |
| C22×#14555772 | 2 |
| #22581517 | 2 |
| #22581098 | 2 |
| #22581092 | 2 |
| #22580962 | 2 |
| #22580949 | 2 |
| #22580920 | 2 |
| C2×2−1+4×C139 | 2 |
| #3010 | 139 |