Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
340 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581321 | C2 | semidirect |
| 3. #22581303 | C2 | semidirect |
| 4. #22581260 | C2 | semidirect |
| 5. #22581248 | C2 | semidirect |
| 8. #22581084 | C2 | semidirect |
| 11. #557×C139 | C2 | semidirect |
| 116. C139 | #3372 | semidirect |
| 118. #557 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581663 | 2 |
| #22581321 | 2 |
| #22581303 | 2 |
| #22581260 | 2 |
| #22581248 | 2 |
| #22581155 | 2 |
| #22581084 | 2 |
| #22581051 | 2 |
| C4×#14555772 | 2 |
| #557×C139 | 2 |
| #3372 | 139 |