Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 5. #22581236 | C2 | semidirect |
| 6. #22581161 | C2 | semidirect |
| 8. #22581060 | C2 | semidirect |
| 9. #22581057 | C2 | semidirect |
| 127. C139 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581505 | 2 |
| C2×Q8×Dic139 | 2 |
| #22581284 | 2 |
| #22581281 | 2 |
| #22581236 | 2 |
| #22581161 | 2 |
| #22581109 | 2 |
| #22581060 | 2 |
| #22581057 | 2 |
| #22581007 | 2 |
| #451×C139 | 2 |
| #3113 | 139 |