Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #22581683 | C2 | semidirect |
| 3. #22581298 | C2 | semidirect |
| 4. #22581241 | C2 | semidirect |
| 5. #22581240 | C2 | semidirect |
| 6. #22581152 | C2 | semidirect |
| 7. #22581150 | C2 | semidirect |
| 8. C8×Dic278 | C2 | semidirect |
| 9. #22581044 | C2 | semidirect |
| 10. C4×#14555774 | C2 | semidirect |
| 11. #486×C139 | C2 | semidirect |
| 77. Dic278 | SD16 | semidirect |
| 78. Dic278 | #41 | semidirect |
| 125. C139 | #3362 | semidirect |
| 130. #486 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581683 | 2 |
| #22581623 | 2 |
| #22581298 | 2 |
| #22581241 | 2 |
| #22581240 | 2 |
| #22581152 | 2 |
| #22581150 | 2 |
| C8×Dic278 | 2 |
| #22581044 | 2 |
| C4×#14555774 | 2 |
| #486×C139 | 2 |
| #3362 | 139 |