Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581623 | C2 | semidirect |
| 3. #22581276 | C2 | semidirect |
| 4. #22581245 | C2 | semidirect |
| 5. #22581188 | C2 | semidirect |
| 6. #22581145 | C2 | semidirect |
| 7. #22581099 | C2 | semidirect |
| 8. C4×#14555774 | C2 | semidirect |
| 9. C8×D556 | C2 | semidirect |
| 10. #22580946 | C2 | semidirect |
| 11. #486×C139 | C2 | semidirect |
| 132. C139 | #3305 | semidirect |
| 136. #486 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581669 | 2 |
| #22581623 | 2 |
| #22581276 | 2 |
| #22581245 | 2 |
| #22581188 | 2 |
| #22581145 | 2 |
| #22581099 | 2 |
| C4×#14555774 | 2 |
| C8×D556 | 2 |
| #22580946 | 2 |
| #486×C139 | 2 |
| #3305 | 139 |