Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #22581506 | C2 | semidirect |
| 3. #22581320 | C2 | semidirect |
| 4. #22581316 | C2 | semidirect |
| 5. #22581314 | C2 | semidirect |
| 6. #22581311 | C2 | semidirect |
| 7. #22580950 | C2 | semidirect |
| 8. #22580949 | C2 | semidirect |
| 9. #22580947 | C2 | semidirect |
| 10. C2×#17984752 | C2 | semidirect |
| 11. #416×C139 | C2 | semidirect |
| 125. C139 | #3135 | semidirect |
| 136. #416 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581506 | 2 |
| #22581499 | 2 |
| #22581320 | 2 |
| #22581316 | 2 |
| #22581314 | 2 |
| #22581311 | 2 |
| #22580950 | 2 |
| #22580949 | 2 |
| #22580947 | 2 |
| C2×#17984752 | 2 |
| #416×C139 | 2 |
| #3135 | 139 |