Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22581686 | C2 | semidirect |
| 2. #22581341 | C2 | semidirect |
| 3. #22581337 | C2 | semidirect |
| 4. #22581174 | C2 | semidirect |
| 5. #22581168 | C2 | semidirect |
| 6. #22581147 | C2 | semidirect |
| 7. #22581083 | C2 | semidirect |
| 8. #22581052 | C2 | semidirect |
| 9. C4×D8×C139 | C2 | semidirect |
| 108. C139 | #3403 | semidirect |
| 118. C4×D8 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581686 | 2 |
| #22581341 | 2 |
| #22581337 | 2 |
| #22581174 | 2 |
| #22581168 | 2 |
| #22581147 | 2 |
| #22581083 | 2 |
| #22581052 | 2 |
| C4×D8×C139 | 2 |
| #3403 | 139 |