Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#17984874 | C2 | semidirect |
| 3. C22⋊Q8×D139 | C2 | semidirect |
| 4. #22581118 | C2 | semidirect |
| 5. #22581114 | C2 | semidirect |
| 6. #22581109 | C2 | semidirect |
| 7. #22581106 | C2 | semidirect |
| 8. #22581103 | C2 | semidirect |
| 9. #22580953 | C2 | semidirect |
| 10. #22580915 | C2 | semidirect |
| 11. #451×C139 | C2 | semidirect |
| 17. C2×Q8×D139 | C22 | semidirect |
| 23. C2×#14555775 | C22 | semidirect |
| 24. C2×#14555774 | C22 | semidirect |
| 25. C2×#14555772 | C22 | semidirect |
| 26. C2×#14555768 | C22 | semidirect |
| 27. #17984822 | C22 | semidirect |
| 31. #17984818 | C22 | semidirect |
| 33. C4⋊C4×D139 | C22 | semidirect |
| 35. #17984766 | C22 | semidirect |
| 36. #17984764 | C22 | semidirect |
| 37. #17984762 | C22 | semidirect |
| 39. (C2×D139)⋊C8 | C22 | semidirect |
| 41. C2×Q16×C139 | C22 | semidirect |
| 43. #103×C139 | C22 | semidirect |
| 142. C22×C139 | #137 | semidirect |
| 171. C139 | #3007 | semidirect |
| 179. #451 | D139 | semidirect |
| 197. C2×Q16 | C2×D139 | semidirect |
| 211. #103 | C2×D139 | semidirect |
| 325. C22 | #17984874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555786 | 2 |
| C2×#17984874 | 2 |
| C22⋊Q8×D139 | 2 |
| #22581118 | 2 |
| #22581114 | 2 |
| #22581109 | 2 |
| #22581106 | 2 |
| #22581103 | 2 |
| #22580953 | 2 |
| #22580915 | 2 |
| #451×C139 | 2 |
| #3007 | 139 |