Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. C2×#17984863 | C2 | semidirect |
| 2. #22581607 | C2 | semidirect |
| 3. #22581606 | C2 | semidirect |
| 4. #22581332 | C2 | semidirect |
| 5. #22581193 | C2 | semidirect |
| 6. #22581159 | C2 | semidirect |
| 7. #22581118 | C2 | semidirect |
| 8. #22581112 | C2 | semidirect |
| 9. C4×#14555770 | C2 | semidirect |
| 10. #22581018 | C2 | semidirect |
| 11. #461×C139 | C2 | semidirect |
| 58. #14555770 | D4 | semidirect |
| 126. C4×C139 | #135 | semidirect |
| 138. C139 | #3283 | semidirect |
| 146. #461 | D139 | semidirect |
| 268. C4 | #17984863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984863 | 2 |
| #22581607 | 2 |
| #22581606 | 2 |
| #22581332 | 2 |
| #22581193 | 2 |
| #22581159 | 2 |
| #22581118 | 2 |
| #22581112 | 2 |
| C4×#14555770 | 2 |
| #22581018 | 2 |
| #461×C139 | 2 |
| #3283 | 139 |