Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4⋊Q8×D139 | C2 | semidirect |
| 3. #22581315 | C2 | semidirect |
| 4. #22581313 | C2 | semidirect |
| 5. #22581312 | C2 | semidirect |
| 6. #22581302 | C2 | semidirect |
| 7. #22581298 | C2 | semidirect |
| 8. #22580953 | C2 | semidirect |
| 9. #22580951 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #489×C139 | C2 | semidirect |
| 140. C139 | #3141 | semidirect |
| 147. #489 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581502 | 2 |
| C4⋊Q8×D139 | 2 |
| #22581315 | 2 |
| #22581313 | 2 |
| #22581312 | 2 |
| #22581302 | 2 |
| #22581298 | 2 |
| #22580953 | 2 |
| #22580951 | 2 |
| #22580905 | 2 |
| #489×C139 | 2 |
| #3141 | 139 |