Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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 |
|---|---|---|
| 3. #22580911 | C2 | semidirect |
| 4. #22580908 | C2 | semidirect |
| 5. M16×Dic139 | C2 | semidirect |
| 6. C2×#17984752 | C2 | semidirect |
| 8. #17984849 | C4 | semidirect |
| 21. #131×C139 | C4 | semidirect |
| 25. #14555769 | C2×C4 | semidirect |
| 26. C2×C139⋊C8 | C2×C4 | semidirect |
| 39. M16×C139 | C2×C4 | semidirect |
| 40. C2×C8×C139 | C2×C4 | semidirect |
| 68. C139 | #2875 | semidirect |
| 79. #131 | Dic139 | semidirect |
| 100. M16 | C2×Dic139 | semidirect |
| 104. C2×C8 | C2×Dic139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984849 | 2 |
| #41×Dic139 | 2 |
| #22580911 | 2 |
| #22580908 | 2 |
| M16×Dic139 | 2 |
| C2×#17984752 | 2 |
| C2×#131×C139 | 2 |
| #2875 | 139 |