Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581669 | C2 | semidirect |
| 2. #22581606 | C2 | semidirect |
| 3. #22581279 | C2 | semidirect |
| 4. #22581273 | C2 | semidirect |
| 5. #22581240 | C2 | semidirect |
| 6. #22581230 | C2 | semidirect |
| 7. #22581207 | C2 | semidirect |
| 8. C4×D1112 | C2 | semidirect |
| 9. #22581032 | C2 | semidirect |
| 10. #22580992 | C2 | semidirect |
| 11. #498×C139 | C2 | semidirect |
| 101. C8×C139 | #41 | semidirect |
| 127. C139 | #3354 | semidirect |
| 131. #498 | D139 | semidirect |
| 229. C8 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581669 | 2 |
| #22581606 | 2 |
| #22581279 | 2 |
| #22581273 | 2 |
| #22581240 | 2 |
| #22581230 | 2 |
| #22581207 | 2 |
| C4×D1112 | 2 |
| #22581032 | 2 |
| #22580992 | 2 |
| #498×C139 | 2 |
| #3354 | 139 |