Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
356 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22581676 | C2 | semidirect |
| 2. #22581347 | C2 | semidirect |
| 4. #22581176 | C2 | semidirect |
| 6. #22581164 | C2 | semidirect |
| 7. #22581055 | C2 | semidirect |
| 8. C4×Dic556 | C2 | semidirect |
| 9. #446×C139 | C2 | semidirect |
| 102. C139 | #3402 | semidirect |
| 110. #446 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581676 | 2 |
| #22581347 | 2 |
| #22581337 | 2 |
| #22581176 | 2 |
| #22581169 | 2 |
| #22581164 | 2 |
| #22581055 | 2 |
| C4×Dic556 | 2 |
| #446×C139 | 2 |
| #3402 | 139 |