Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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×#17984801 | C2 | semidirect |
| 3. #22581295 | C2 | semidirect |
| 4. #22581289 | C2 | semidirect |
| 5. #22581284 | C2 | semidirect |
| 6. #22581278 | C2 | semidirect |
| 7. #22581272 | C2 | semidirect |
| 8. #22581267 | C2 | semidirect |
| 9. #22580991 | C2 | semidirect |
| 10. #22580950 | C2 | semidirect |
| 11. C2×C22⋊C8×C139 | C2 | semidirect |
| 30. #17984776 | C22 | semidirect |
| 31. #17984776 | C22 | semidirect |
| 32. #17984774 | C22 | semidirect |
| 33. #17984774 | C22 | semidirect |
| 34. #17984767 | C22 | semidirect |
| 35. #17984767 | C22 | semidirect |
| 36. #17984764 | C22 | semidirect |
| 37. #17984764 | C22 | semidirect |
| 143. C139 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581464 | 2 |
| C2×#17984801 | 2 |
| #22581295 | 2 |
| #22581289 | 2 |
| #22581284 | 2 |
| #22581278 | 2 |
| #22581272 | 2 |
| #22581267 | 2 |
| #22580991 | 2 |
| #22580950 | 2 |
| C2×C22⋊C8×C139 | 2 |
| #3091 | 139 |