Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 4. #22581239 | C2 | semidirect |
| 5. #22581238 | C2 | semidirect |
| 6. #22581160 | C2 | semidirect |
| 8. #22581060 | C2 | semidirect |
| 9. #22581057 | C2 | semidirect |
| 11. #462×C139 | C2 | semidirect |
| 132. C139 | #3113 | semidirect |
| 140. #462 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| C4×Q8×D139 | 2 |
| #22581282 | 2 |
| #22581239 | 2 |
| #22581238 | 2 |
| #22581160 | 2 |
| #22581107 | 2 |
| #22581060 | 2 |
| #22581057 | 2 |
| #22581009 | 2 |
| #462×C139 | 2 |
| #3113 | 139 |