Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #22581315 | C2 | semidirect |
| 3. #22581310 | C2 | semidirect |
| 4. #22580961 | C2 | semidirect |
| 6. C4×#14555769 | C2 | semidirect |
| 7. #533×C139 | C2 | semidirect |
| 15. #17984765 | C22 | semidirect |
| 17. #17984753 | C22 | semidirect |
| 18. C4×C139⋊C8 | C22 | semidirect |
| 19. C4⋊Q8×C139 | C22 | semidirect |
| 20. #125×C139 | C22 | semidirect |
| 83. C139 | #3140 | semidirect |
| 85. #533 | D139 | semidirect |
| 95. C4⋊Q8 | C2×D139 | semidirect |
| 96. #125 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984830 | 2 |
| #22581315 | 2 |
| #22581310 | 2 |
| #22580961 | 2 |
| #22580957 | 2 |
| C4×#14555769 | 2 |
| #533×C139 | 2 |
| #3140 | 139 |