Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581271 | C2 | semidirect |
| 3. #22581243 | C2 | semidirect |
| 4. #22581148 | C2 | semidirect |
| 5. #22581087 | C2 | semidirect |
| 6. #22581063 | C2 | semidirect |
| 7. #22581010 | C2 | semidirect |
| 8. C2×C4×D4×C139 | C2 | semidirect |
| 11. #17984842 | C22 | semidirect |
| 12. #17984839 | C22 | semidirect |
| 17. C4×D556 | C22 | semidirect |
| 18. #17984773 | C22 | semidirect |
| 19. C4⋊(C139⋊C8) | C22 | semidirect |
| 21. #17984762 | C22 | semidirect |
| 23. #17984753 | C22 | semidirect |
| 81. D4×C139 | #41 | semidirect |
| 120. C139 | #3109 | semidirect |
| 123. C2×C4×D4 | D139 | semidirect |
| 199. D4 | #14555785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| #22581271 | 2 |
| #22581243 | 2 |
| #22581148 | 2 |
| #22581087 | 2 |
| #22581063 | 2 |
| #22581010 | 2 |
| C2×C4×D4×C139 | 2 |
| #3109 | 139 |