Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 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×#17984850 | C2 | semidirect |
| 3. #22581074 | C2 | direct (N × H) |
| 4. C2×#17984768 | C2 | semidirect |
| 5. C2×#17984752 | C2 | semidirect |
| 6. C2×#108×C139 | C2 | semidirect |
| 8. #17984864 | C4 | semidirect |
| 10. C2×Dic556 | C4 | semidirect |
| 11. C2×#14555774 | C4 | semidirect |
| 12. C2×D1112 | C4 | semidirect |
| 14. #17984850 | C22 | semidirect |
| 19. #17984768 | C22 | semidirect |
| 20. #17984752 | C22 | semidirect |
| 23. #108×C139 | C22 | semidirect |
| 33. Dic556 | C2×C4 | semidirect |
| 34. #14555774 | C2×C4 | semidirect |
| 35. D1112 | C2×C4 | semidirect |
| 88. C2×C139 | #444 | semidirect |
| 91. C139 | C2×#444 | semidirect |
| 96. C2×#108 | D139 | semidirect |
| 113. #108 | C2×D139 | semidirect |
| 181. C2 | #22581074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| C2×#17984850 | 2 |
| #22581074 | 2 |
| C2×#17984768 | 2 |
| C2×#17984752 | 2 |
| C2×#108×C139 | 2 |
| C2×#444 | 139 |