Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581508 | C2 | semidirect |
| 3. #22581320 | C2 | semidirect |
| 4. #22581316 | C2 | semidirect |
| 5. #22581315 | C2 | semidirect |
| 6. #22581313 | C2 | semidirect |
| 7. #22581312 | C2 | semidirect |
| 8. #22580948 | C2 | semidirect |
| 9. #22580946 | C2 | semidirect |
| 10. #97×D139 | C2 | semidirect |
| 11. #489×C139 | C2 | semidirect |
| 137. C139 | #3135 | semidirect |
| 146. #489 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #22581502 | 2 |
| #22581320 | 2 |
| #22581316 | 2 |
| #22581315 | 2 |
| #22581313 | 2 |
| #22581312 | 2 |
| #22580948 | 2 |
| #22580946 | 2 |
| #97×D139 | 2 |
| #489×C139 | 2 |
| #3135 | 139 |