Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581503 | C2 | semidirect |
| 2. #22581487 | C2 | semidirect |
| 3. #22581362 | C2 | semidirect |
| 4. #22581342 | C2 | semidirect |
| 5. #22581318 | C2 | semidirect |
| 6. #22581313 | C2 | semidirect |
| 7. #22581206 | C2 | semidirect |
| 8. #22581199 | C2 | semidirect |
| 9. C4×#14555774 | C2 | semidirect |
| 10. C4×D1112 | C2 | semidirect |
| 11. C4×M16×C139 | C2 | semidirect |
| 110. C8×C139 | #41 | semidirect |
| 137. C139 | #3171 | semidirect |
| 149. C4×M16 | D139 | semidirect |
| 248. C8 | #14555785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| #22581487 | 2 |
| #22581362 | 2 |
| #22581342 | 2 |
| #22581318 | 2 |
| #22581313 | 2 |
| #22581206 | 2 |
| #22581199 | 2 |
| C4×#14555774 | 2 |
| C4×D1112 | 2 |
| C4×M16×C139 | 2 |
| #3171 | 139 |