Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 382 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. #22581678 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581255 | C2 | semidirect |
| 5. #22581230 | C2 | semidirect |
| 6. #22581152 | C2 | semidirect |
| 7. #22581150 | C2 | semidirect |
| 8. #22581083 | C2 | semidirect |
| 9. #22581050 | C2 | semidirect |
| 10. C4×#14555774 | C2 | semidirect |
| 11. #486×C139 | C2 | semidirect |
| 77. Dic278 | #41 | semidirect |
| 124. C139 | #3368 | semidirect |
| 129. #486 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581678 | 2 |
| #22581623 | 2 |
| #22581316 | 2 |
| #22581255 | 2 |
| #22581230 | 2 |
| #22581152 | 2 |
| #22581150 | 2 |
| #22581083 | 2 |
| #22581050 | 2 |
| C4×#14555774 | 2 |
| #486×C139 | 2 |
| #3368 | 139 |