Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17984865 | C2 | semidirect |
| 2. C22×C8×D139 | C2 | semidirect |
| 3. #22581466 | C2 | semidirect |
| 4. #22581191 | C2 | semidirect |
| 5. #22581190 | C2 | semidirect |
| 6. #22581189 | C2 | semidirect |
| 7. #22581185 | C2 | semidirect |
| 8. #22581184 | C2 | semidirect |
| 9. #22580990 | C2 | semidirect |
| 10. #22580948 | C2 | semidirect |
| 11. #467×C139 | C2 | semidirect |
| 15. C2×#14555772 | C22 | semidirect |
| 16. C2×D1112 | C22 | semidirect |
| 31. #17984776 | C22 | semidirect |
| 32. #17984773 | C22 | semidirect |
| 33. #17984766 | C22 | semidirect |
| 34. #17984764 | C22 | semidirect |
| 35. #17984762 | C22 | semidirect |
| 36. C2×Q16×C139 | C22 | semidirect |
| 39. #107×C139 | C22 | semidirect |
| 40. #103×C139 | C22 | semidirect |
| 64. C8×D139 | D4 | semidirect |
| 118. C22×C139 | #135 | semidirect |
| 129. C2×D139 | #135 | semidirect |
| 145. C139 | #3050 | semidirect |
| 151. #467 | D139 | semidirect |
| 161. C2×Q16 | C2×D139 | semidirect |
| 181. #107 | C2×D139 | semidirect |
| 184. #103 | C2×D139 | semidirect |
| 274. C22 | #17984865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| C22×C8×D139 | 2 |
| #22581466 | 2 |
| #22581191 | 2 |
| #22581190 | 2 |
| #22581189 | 2 |
| #22581185 | 2 |
| #22581184 | 2 |
| #22580990 | 2 |
| #22580948 | 2 |
| #467×C139 | 2 |
| #3050 | 139 |