Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4×Q8×D139 | C2 | semidirect |
| 3. #22581268 | C2 | semidirect |
| 4. #22581245 | C2 | semidirect |
| 5. #22581154 | C2 | semidirect |
| 6. #22581153 | C2 | semidirect |
| 7. #22581093 | C2 | semidirect |
| 8. #22581056 | C2 | semidirect |
| 9. #22581052 | C2 | semidirect |
| 10. #22581009 | C2 | semidirect |
| 11. #477×C139 | C2 | semidirect |
| 87. Dic278 | #41 | semidirect |
| 108. Q8×C139 | #41 | semidirect |
| 140. C139 | #3112 | semidirect |
| 146. #477 | D139 | semidirect |
| 231. Q8 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581504 | 2 |
| C4×Q8×D139 | 2 |
| #22581268 | 2 |
| #22581245 | 2 |
| #22581154 | 2 |
| #22581153 | 2 |
| #22581093 | 2 |
| #22581056 | 2 |
| #22581052 | 2 |
| #22581009 | 2 |
| #477×C139 | 2 |
| #3112 | 139 |