Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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. #22581688 | C2 | semidirect |
| 2. #22581625 | C2 | semidirect |
| 3. #22581342 | C2 | semidirect |
| 4. #22581330 | C2 | semidirect |
| 5. #22581169 | C2 | semidirect |
| 6. #22581154 | C2 | semidirect |
| 7. #22581149 | C2 | semidirect |
| 8. #22581149 | C2 | semidirect |
| 9. #22581066 | C2 | semidirect |
| 10. C4×#14555774 | C2 | semidirect |
| 11. #446×C139 | C2 | semidirect |
| 108. C8×C139 | #41 | semidirect |
| 134. C139 | #3399 | semidirect |
| 144. #446 | D139 | semidirect |
| 243. C8 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581625 | 2 |
| #22581342 | 2 |
| #22581330 | 2 |
| #22581169 | 2 |
| #22581154 | 2 |
| #22581149 | 2 |
| #22581066 | 2 |
| C4×#14555774 | 2 |
| #446×C139 | 2 |
| #3399 | 139 |