Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 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. #22581349 | C2 | semidirect |
| 3. #22581291 | C2 | semidirect |
| 4. #22581283 | C2 | semidirect |
| 5. #22581245 | C2 | semidirect |
| 6. #22581238 | C2 | semidirect |
| 7. #22581209 | C2 | semidirect |
| 8. C4×#14555775 | C2 | semidirect |
| 10. #22580993 | C2 | semidirect |
| 116. C139 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581673 | 2 |
| #22581349 | 2 |
| #22581291 | 2 |
| #22581283 | 2 |
| #22581245 | 2 |
| #22581238 | 2 |
| #22581209 | 2 |
| C4×#14555775 | 2 |
| #22581031 | 2 |
| #22580993 | 2 |
| #554×C139 | 2 |
| #3356 | 139 |