Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22581622 | C2 | semidirect |
| 3. #22581328 | C2 | semidirect |
| 4. #22581189 | C2 | semidirect |
| 5. #22581186 | C2 | semidirect |
| 6. #22581151 | C2 | semidirect |
| 7. #22581098 | C2 | semidirect |
| 8. #22581097 | C2 | semidirect |
| 9. Q16×Dic139 | C2 | semidirect |
| 10. C8×C22⋊D139 | C2 | semidirect |
| 11. C2×#135×C139 | C2 | semidirect |
| 74. Q16×C139 | D4 | semidirect |
| 134. Dic139 | #135 | semidirect |
| 142. C139 | #3287 | semidirect |
| 145. C2×#135 | D139 | semidirect |
| 202. Q16 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| #22581622 | 2 |
| #22581328 | 2 |
| #22581189 | 2 |
| #22581186 | 2 |
| #22581151 | 2 |
| #22581098 | 2 |
| #22581097 | 2 |
| Q16×Dic139 | 2 |
| C8×C22⋊D139 | 2 |
| C2×#135×C139 | 2 |
| #3287 | 139 |