Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581503 | C2 | semidirect |
| 2. C4×#14555785 | C2 | semidirect |
| 3. #22581278 | C2 | semidirect |
| 4. #22581239 | C2 | semidirect |
| 5. #22581234 | C2 | semidirect |
| 6. #22581154 | C2 | semidirect |
| 7. #22581149 | C2 | semidirect |
| 8. #22581100 | C2 | semidirect |
| 9. #22581066 | C2 | semidirect |
| 10. #22581055 | C2 | semidirect |
| 11. #432×C139 | C2 | semidirect |
| 87. Dic278 | #41 | semidirect |
| 93. D556 | #41 | semidirect |
| 144. C139 | #3115 | semidirect |
| 156. #432 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| C4×#14555785 | 2 |
| #22581278 | 2 |
| #22581239 | 2 |
| #22581234 | 2 |
| #22581154 | 2 |
| #22581149 | 2 |
| #22581100 | 2 |
| #22581066 | 2 |
| #22581055 | 2 |
| #432×C139 | 2 |
| #3115 | 139 |